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Dissertations and Theses Dissertations and Theses

1-1-1987

Interregional Competition in the Wood Products Interregional Competition in the Wood Products

Industry: An Econometric Spatial Equilibrium Industry: An Econometric Spatial Equilibrium

Approach Approach

M. Hossein Haeri Portland State University

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Recommended Citation Recommended Citation Haeri, M. Hossein, "Interregional Competition in the Wood Products Industry: An Econometric Spatial Equilibrium Approach" (1987). Dissertations and Theses. Paper 539. https://doi.org/10.15760/etd.539

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INTERREGIONAL COMPETITION IN THE WOOD PRODUCTS INDUSTRY:

AN ECONOMETRIC SPATIAL EQUILIBRIUM APPROACH

by

M. HOSSEIN HAERI

A dissertation submitted in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY in

URBAN STUDIES: REGIONAL SCIENCE

Portland State University

1987

TO THE OFFICE OF GRADUATE STUDIES AND RESEARCH

The members of the committee approved the dissertation

of M. Hossein Haeri presented May 21, 1987.

Anthony M. Rufolo, Chairman

APPROVED:

Public Affairs

Bernard Ross, Dean of Graduate Studies and Research

AN ABSTRACT OF THE DISSERTATION OF M. Hossein Haeri for the

Doctor of Philosophy in Urban Studies: Regional Science

preserited May 21, 1987.

Title: Interregional Competition in the Wood Products

Industry: An Econometric spatial Equilibrium

Approach.

APPROVED BY MEMBERS OF THE DISSERTATION COMMITTEE:

~eSlG: Strathman

This study presents a multiregional model of the soft­

wood forest products industry in the united States, designed

to describe the dynamics of interregional competition in the

industry and to provide a means for policy experimentation

and short-term projection of regional market shares. Two

2

products (softwood lumber and plywood), five product supply

regions (including Canada), and six product

are recognized. The design of the model

demand regions

is based on a

combined top-down/bot tom-up approach and consists of three

interdependent components: 1) the aggregate product market,

2) regional product markets, and 3) regional factor markets.

Model solutions are obtained by the simultaneous

determination of national level product prices and quanti­

ties and allocation of equilibrium quantities across

producing regions on the basis of their relative prices and

locational advantage.

The model is evaluated in an historical simulation

using data for 1950-84. Graphical analysis of simulated

series suggests that the model replicates short-run trends

as well as cyclical movements in aggregate demand and

regional market shares. The results indicate that the short­

run impacts of relative prices and locational advantage

on regional market shares are generally small. Price respon­

siveness of regional market shares for lumber appear to be

considerably lower than that of plywood, indicating greater

degrees of regional sUbstitution in the plywood market.

The forecasting application of the model is demons­

trated by extrapolating the complete structure for two years

beyond the sample period. The projected trend during this

two-year period is one of increasing demand for both lumber

and plywood. Domestic producers' shares of the lumber market

are expected to remain relatively stable. The results show

3

that nearly all increases in demand for lumber in this

period will be satisfied by Canadian imports.

ACKNOWLEDGEMENTS

All credit for this work is shared in equal propor­

tions with my wife Mary and my daughter Mana. Without their

affectionate support and unyielding patience, I could have

never completed t.his work.

I am indebted to professors Anthony Rufolo and James

Strathman, teachers and friends, who inspired and guided me

throughout my graduate studies at Portland State University.

They helped me overcome my ignorance in many areas of

regional economics without compromising my self confidence.

My enduring gratitude goes to Dr. Richard Haynes of

the Pacific Northwest Forest and Range Experiment station in

Portland for giving me so much of his valuable time whenever

I needed it; and for his many scholarly works that lit my

way through the deep forests of the wood products economy.

Professors Tom Potiowsky and Giles Burgess of the

Economics Department at Portland State University provided

many valuable comments on earlier drafts of this document.

I also acknowledge with gratitude the receipt of

financial assistance from the School of Urban and Public

Affairs during the course of my graduate studies at Portland

State University.

TABLE OF CONTENTS

PAGE

ACKNOWLEDGEMENTS ....••.•.............•.•.....•.•..•.. iii

LIST OF TABLES ..•...•.•....•••.•.•..••.•....•...•.... vi

LIST OF FIGURES •.......•.•.••.••.••.•••....•••.••••.. viii

CHAPTER

I INTRODUCTION.... • . . . • • • • • • . • . • . • . • • • • • • . • . . • 1

The Methodological Perspective •••..••.•.. 4

The Theoretical Framework •...•..•...•..•• 7

Product Demand Demand for Regional Products Regional Product Supply Regional Factor Markets The Complete Model

II THE INDUSTRY ••..•••.•.••••..•...•..•.......• 24

The Structure of the Industry............ 25

The Market Process •••••••••.••..••.•••.•. 27

The Spatial Dimension •••.•...••..••.••... 32

Regional Market Shares ••.•••••••••••••.•. 35

Regional Timber Resources................. 42

III THE EMPIRICAL MODEL •.••••••..•.•...•...••..• 52

The Model, Its Structure, and Components. 55

Model Estimation •••..•••.•.•••..••••••..• 58

v

CHAPTER PAGE

Model Components ••••..•.••.••..••.•.••... 68

The Aggregate Product Market Regional stumpage Markets Regional Product Markets Regional Market Shares

IV MODEL VALIDATION ............................ 89

Validation in Parameter Estimates .•••..•. 89

Validation in simulation and Forecasting. 97

Concluding Remarks ••••.•••.••.••••..•.•.• 115

LITERATURE CITED

APPENDIX A: Data Sources ............................ .

APPENDIX B: Average Hourly Earnings in Manufacturing

118

125

and Lumber & Wood Products •••••••.••••••. 127

APPENDIX C: Labor productivity in Lumber and Plywood Production ............................... 128

APPENDIX 0: Producer Price Indexes for Transportation services and Lumber & Wood Products Freight ........ 1 • • • • • • • • • • • • • • • • • • • • • • • • • 129

TABLE

I

II

LIST OF TABLES

Domestic Lumber consumption by End Use category (Percent of Total Consumption)

Lumber and Plywood Production Processes

III Regional Lumber Market Shares

PAGE

28

30

(% Total Consumption) ••••.•••.••.•..••.•..••.. 36

IV Regional Plywood Market Shares (% Total Consumption) .••••••••••.••..•••.••..• 39

V Distribution of Timberlands by Region and Ownership in 1977 (MM Acres) •••••.•....•••••.• 44

VI Annual Harvest of Softwood Timber by Region and Ownership (1950-1984) ••••••••.••....•..•.• 48

VII Volume of Softwood Sawtimber by Region and Ownership 1977 (MM BFt.) ••••••.•.••...••.•••.• 50

VIII

IX

X

Parameter Estimates of the Model .............. Description of Variables Used in the Model ••..

Estimation Results for Regional Stumpage Price Relationships ................................ .

XI Estimates of Regional Elasticities of Private

60

64

75

stumpage Supply ............................... 77

XII Interregional Transport Costs for Lumber 1977 ($ per MBFt. Deflated) •••...•.....••..••. 87

XIII Interregional Tra~sport Costs for Plywood 1977 ($ per MBFt. Deflated) •••••.•.•••..••••• 87

XIV Regional Indexes of Accessibility Lumber and Plywood ............. .,.............. 88

xv Impact Multipliers for Selected Explanatory variables: Regional Lumber output (Measured as % of Total Consumption) .•.••••.••••.•..•••..••...• 93

TABLE

XVI

vii

PAGE

Impact Nultipliers for Selected Explanatory Variables: Regional Lumber Market Shares ..•....... 95

XVII Projected Values for Major Softwood Lumber and Plywood Market Variables •...•....••...•....•.. 112

XVIII Average Hourly Earnings in Manufacturing and Lumber & Wood Products ........•...... 127

XIX Labor Productivity in Lumber and Plywood Production ................................... 128

XX Producer Price Index: Transportation Services and Lumber & Wood Products Freight ••..•.•..•. 129

FIGURE

1.

2.

3.

4.

5.

6.

7.

LIST OF FIGURES

Effects of Alternative Assumptions Regarding Elasticities of Supply ••••••..••••......•...•..

Model Flow Schematic •••••.••..•••.•...•.•.•....

Major Products and Stages in the Processing of Timber ................................ ., .... .

Product supply Regions . ....................... . Product Demand Regions II II • II II • II • II II II II II II II II II II II II II • II ••

Regional Market Shares in Lumber as Percent of Apparent consumption (1950-1984) ••••.••.•••••••

Regional Plywood Market Shares as Percent of Apparent Consumption (1950-1984) ••••••••..•...•

PAGE

16

22

26

34

34

40

40

8. Canadian Lumber Production, Consumption and

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

Exports ........................................ 41

Model Structure and Its Main Interactions ••.•••

Historical Simulation Total Lumber consumption •

Historical Simulation Average Lumber Price ..•..

Historical Simulation Total Plywood Consumption

Historical Simulation PPI Softwood Plywood ..•••

Historical Simulation Stumpage Price NW II II II II II II • II

• II II II • II II II

II II II • II II II II

Historical Simulation Stumpage Price SO

Historical Simulation Stumpage Price SW

Historical Simulation Stumpage Price IL

Historical Simulation Lumber Price NW • II II II II II II II II II

Historical Simulation Lumber Price SO

57

98

98

99

99

100

100

101

101

102

102

FIGURE

20.

21-

22.

23.

24.

25.

26.

27.

28.

29.

30.

Historical Simulation Lumber Price SW

Historical Simulation Lumber Price IL •.......•.

Plywood Price Douglas Fir .•••.•..•.•.•....•....

Plywood Price Southern pine .•.••.•.•.•.••.•....

Lumber Market Share Canada •.•.•.••••.•.•.......

Lumber Market Share NW

Lumber Market Share SO

Lumber Market Share SW

Lumber Market Share IL

Plywood Market Share NW

Plywood Market Share SO

· ....................... . · ....................... . · ....................... . · ....................... . . ...................... . . ...................... .

ix

PAGE

103

103

104

104

105

105

106

106

107

107

108

31. Lumber Market Share North ••.•.•••••..••.••..••• 108

This

separated

CHAPl'ER I

INTRODUCTION

is a study

markets. It

of competition

concerns the

among spatially

development and

estimation of a multiregional model of the softwood forest

products industry in the United states, designed to

describe the dynamics of interregional competition in the

industry; and to provide a means for policy experimenta­

tion and short-term projection of regional market

shares.

The study is motivated by an interest to find out,

given information on the aggregate national demand for these

products, how production would be allocated among spatially

separate producers. Two products (softwood lumber and

plywood), five product supply regions (including Canada),

and six product demand regions are recognized. The design

of the model is based on a combined top-down/bot tom-up

approach and consists of three interdependent components:

1) the aggregate product market, 2) regional product

markets, and 3) regional factor markets.

Model solutions are obtained by the simUltaneous

determination of national level product prices and quanti­

ties; and allocation of equilibrium quantities across

2

producing regions on the basis of their relative prices and

locational advantage. For each producing region, "locational

advantage" is measured in terms of the region's overall

accessibility in the national market.

A thirty-five year period time series data from 1950

to 1984 is used to estimate the parameters of the model.

Following an assessment of the performance of the model, the

complete structure is then extrapolated for two years beyond

the sample period.

The first step in an empirical investigation is to

identify the perspective from which it originates, and to

define explicitly the theoretical framework in which the

results may be deciphered. The principal mode of analysis

adopted here is general equilibrium. The approach can be

best described as an eclectic one: we draw from various

areas of economic thought bordering on the neo-classical

orientation, in particular, international trade and location

theory.

The perspective here is that of the analyst interested

in the dynamics of interregional competition and short-term

forecast of regional export performance. Since the approach

adopted in this study recognizes the impacts of exogenous

demand and local supply conditions simultaneously, it

presents a suitable alternative to such naive devices as

regional "shift-share" and, its counterpart in inter-

national trade, "constant market-share analysis" and serve

3

as a versatile tool for policy simulation. 1

The organization of this thesis is in four parts. The

first chapter begins by casting the research problem in the

general theoretical framework of interregional competition.

We will then proceed to explore the required methods and

necessary ingredients for developing a multiregional

industry model.

The second chapter is intended to serve as an

introduction to the forest products industry. Here, various

economic, spatial, and institutional aspects of the industry

will be examined in some detail. Institutional fa:.:tors will

be discussed only to the extent that they contribute to

behavioral variations in regional markets. We shall make no

attempt to partake in the ongoing controversy that surrounds

the issue of public policy in this area. In this part of the

study we will also specify the spatial units of our analysis

(regions), consider their characteristics and describe the

qualitative and quantitative differences that prevail among

them in terms of resource endowment and ability to grow,

process, and market their products.

1 We do not purport to discuss these techniques at any length here or elsewhere in this document. Richardson (1978) contains an ample discussion on the theory and application of "shift-share" analysis in regional studies. See also Houston (1967) for a critical treatment of the concept. For an exposition of "constant market share" analysis in international trade and a bibliography of empirical applications of the approach the reader is referred to Leamer and Stern (1970) pp.171-82.

4

Chapter III presents a summary review of previous

attempts at modeling the timber industry and use whatever

insight that can be drawn from them in developing estimating

relationships for the empirical model. In this part of the

study, after considering relevant statistical and method-

ological issues, the complete empirical model will be

estimated. Chapter IV, the final part of the study, is

devoted entirely to the analysis of results and evaluation

of performance of the model.

THE METHODOLOGICAL PERSPECTIVE

The subject of this study bears a prima facie

resemblance to the well-known Enke-Samuelson problem of

equilibrium among spatially separated markets. It seems

therefore helpful at this preliminary stage to distinguish

between the purpose and method of the present study from

those associated with theirs.

The problem of equilibrium among spatially separated

markets was first set forth by Enke in 1951:

••• There are several (originally three) regi~ns trading a homogenous good. Each reg~on constitutes a single and distinct market ••. The regions are separated but not isolated by a transportation cost per unit whic~ is indepen­dent of volume. There are no legal restrictions to limit the actions of the profit-seeking traders in each region. For each region the functions that relate local production and local use to local prices are known, and consequently, the magnitude of the difference which will be exported or imported at each local price is also known. Given these trade functions and transpor­tation costs, we wish to ascertain: (1) the net

price in each region; (2) the quantity of imports oT. exports for each region; (3) which region exports, imports, or does neither; (4) the volume and direction of trade between each possible pair of regions." (Enke 1951)

5

Given linear regional production and demand functions,

and no economies of scale in transportation, Enke conceived

of a solution to this problem by means of an electric

analogue. Samuelson (1952) proceeded with the above

formulation and demonst~ated how it can be cast

mathematically into a maximum problem and sol ved via the

Hitchcock-Koopmans minimum transport cost linear programming

procedure. The procedure consists of an iterative procss of

varying interregional flows towards increasing "net social

payoff" (i.e. the algebraic sum of areas under local excess

supply and demand functions minus total transportation cost

of all possible flows).2

Consequent elaborations of the approach and

development of new solution algorithms have helped extend

its applications to a wide range of analytic situations

concerning temporal, as well as spatial activity and

2 For a non-mathematical discussion of the theory and application of linear programming see Dorfman (1953). Isard (1960, PP. 413-88) contains a compreh~nsive presentation of the technique and solution procedures in mathematical programming. For a more elaborate presentation and alternative formulations of spatial allocation and distribution problems see Takayama and Judge (1971).

6

allocation problems. 3 Developments have been particularly

remarkable in the direction of relaxing the stringent

assumptions of the early formulations concerning quantities

and prices, and especially, linearity of production and

demand functions. contributions of Takayama and Judge

(1964a, 1964b, 1971) have lead to the development of opera-

tional programming models in which prices and quantities are

determined endogenously within the model.

Despite their theoretical elegance and versatility,

most variants of mathematical programming models, save the

very simple single objective linear formulations, pose

serious practical problems when applied to general

equilibrium analysis where large numbers of inputs,

commodities, and locations are involved. In fact

applications of mathematical programming models in spatial

contexts have invariably been cast in a partial equilibrium

framework in which only one sector of the economy or a

limited group of related commodities is considered while the

demand for, and prices, of other goods are determined

3 The first application of linear programming in a spatial allocation setting was made by Fox (1953) in his study of the feed-livestock market in the United states. The method has since been applied to a myriad of agricultural products (See Labys 1975), various natural resource commodities (for example Kennedy 1974), the timber industry (Holley, et al. 1975, Haynes, et al. 1978), and the equilibrium analysis of international trade (Uzawa 1958, Ginsburgh and Waelbroeck 1981).

7

exogenously. And yet, even in these situations the analysis

is often hindered by the complexity of solution schemes.

The purpose of the present study is more modest and,

at the same time, more basic than what most programming

models propose to achieve. The objective of this study,

though not completely at variance with what can be obtained

in a programming approach, differs from it in several

fundamental ways. These differences become more apparent in

the subsequent discussion where we proceed with the develop­

ment of our general theoretical model. For the time being it

suffices to point out that this study intends to investigate

optimization in a more simplified supply-demand framework

which does not concern interregional "flows" as such.

THE THEORETICAL FRAMEWORK

Having defined our objective, we must now explore the

means of achieving it. Again, as with the Enke formulation,

the conceived economic environment is a competitive one in

which several producers are engaged in the production of one

or more homogeneous good(s). Production takes place in

predetermined locations (regions) which are separated from

each other and from consumers by an intervening trans­

portation cost. There are no barriers to trade and local

producers can compete freely in the national market. Given

the level of national demand for a good, we like to find

out: a) how regional output shares will be determined, and

8

b) given any initial equilibrium condition, what the effect

will be on regional output levels of changes in the

aggregate demand or local production conditions. Any

econometric model capable of identifying the unique impacts

of these factors on the regional output shares, must feature

several critical characteristics. As Engle (1979a) has

pointed out --though in a slightly different context-- such

a model must produce reliable estimates of the elasticity of

demand for regional products, determine the impact of

factors on the supply schedule, and estimate the elastici­

ties of factor supplies.

The foregoing conceptual framework embodies several

necessary relationships that must be explicitly specified in

the operational model. These are:

a) aggregate national demand relationship; b) regional product demand relationships that can

determine regional allocations of output on the basis of each region's unique advantage (dis­advantage) in relative cost and location vis-a­vis others;

c) regional product supply relationships; d) regional factor-market relationships; and e) an equilibrium condition that ensures the

consistency between projections at the national level of aggregate demand and regional supplies.

It also implies certain interactions that prevail among

these relationships at the interregional, as well as,

regional-national level which are to be accounted for in the

operational model. Under product market conditions with a

sufficiently large number of agents and perfectly elastic

supplies (as the case is often assumed to be in

9

international trade analysis) we normally need not concern

ourselves with these interactions. In national economies,

however, any analysis advanced on the basis of these

assumptions is likely to fall at the first fence. For one

thing, the number of producing regions for most commodities

is often small and their outputs constitute a large enough

portion of total supply so that the assumption of perfectly

elastic demand would not hold. The proper analytic framework

is therefore a quasi-competitive one where the actions of

anyone producer will have definite repercussions for other

producers (Henderson and Quandt 1980, p.200). For another,

any a priori assumptions concerning regional supply

elasticities may well prove unwarranted.

In sections that follow, we will specify these

relationships separately, elaborate their conceptual content

and theoretical foundations and explore the nature and

direction of their interdependencies.

Product Damand

Specification of demand relationships derives directly

from the general theory of consumer behavior. In its basic

form the theory explains demand as conditions that must be

satisfied if the consumer is to get the most for his money.

Given an index of consumer satisfaction (U), a set of goods

i=l ••• n) and their corresponding prices (p. ~

i=l ••• n), and a budget constraint (Y) for the consumer; the

demand function for any xi can be determined by maximizing

10

U=f (xl' x2'···, xn) subj ect to Y=P1 Xl + P2x2 + ••• + Pnxn•

Assuming that th~ second order conditions are fulfilled, the

first order conditions, together with the Ludget constraint

can produce consumer's n demand functions:

(1.1) for j=1,2, •.. n-1

which relates the demand for a commodity Xi to its own price

the prices of other commodities and income

(Henderson and Quandt, 1980, pp.18-22).

Equation (1.1) represents the general form of the

aggregate national demand relationship in our model.

Replacing Y with a vector of appropriate exogenous variables

Z; and letting Pi equal the weighted average national price

of commodi ty i, we specify the aggregate national demand

relationship in the following form:

(1. 2)

Demand For Regional Products

Equation (1.2) represents the general formulation of

commodity demand functions in a spaceless economy. The

inclusion of a spatial dimension in the analysis will

require certain modifications in this specification in order

to account for distinctions among Xi'S not only in terms of

11

their kind, but also with respect to their places of

production and consumption.

Let us suppose there are n goods being produced in r

regions. The products of each and every region are partially

consumed in the producing region itself and the rest,

assuming the presence of some excess supply, is shipped to

other regions. 4 Any complete model of the national economy,

therefore, will have to account for rn distinct products and

rn prices. That is, for each rXi (where the first subscript

represents the place of production) there will be k

different rPik's where each rPik' i.e. the price in region k

of good i produced in region r, equals the price of that

product in the producing region plus its transfer cost to

the consuming region. In equilibrium, as Samuelson (1952, p.

287) has shown, the unit price of the good in the consuming

region cannot, however, exceed its price in the producing

region plus the per unit transportation cost between the two

regions i. e. :

(1. 3) P'k < p, + t k r ~ - r ~r r

4 In order to avoid confusion, it is helpful at this point to add a slight refinement to our terminology. Here- after, following Armington (1969), we will use the term "goods" to distinguish between commodities in terms of their kind. Alternatively, the term "product" will be used to distinguish between commodities both in terms of kind and the geographic place of production or consumption.

12

from which it follows that we can conceivably define a

demand function for each region!s output, rdi , as:

(1.4) (k=l. •• n)

where k and r respectively represent locations of

consumption and production; and the second term on the right

hand side can be construed as a measure of the producing

region's overall accessibility in the market. 5

The foregoing discussion suggests how the second set

of relationships in our model, i.e. regional allocation of

output, might be derived. The key structural relationship

here is the demand for the regional output. We can expect

the quantity demanded of a product to decrease as its local

price rises. This occurs partly due to income and

sUbstitution effects. However in product markets with

several regional sources of supply, a major effect can

result from the shift to the same product from a different

region (Engle 1979b). One simple formulation of the demand

5 In most models of location analysis it is assumed that transportation inputs are proportional to the quan­tities being shipped implying that there are no economies of scale in transportation. However, in our model, transport inputs will be measured in terms of average per unit transport costs between trading areas, which when available, is a more realistic measure of the friction of distance as compared to transport "rates".

13

function facing a regional product is direct estimation of

every producing region's market share in all demand regions

as a function of its own price and prices of the same good

from alternative sources of supply:

Let rdik denote demand in region k of good i produced

in region r; then for a system of r producing regions and k

consuming regions we will have:

(1. 5)

ldil = f( dil , lPil' 2Pil' 3Pil' ••• , r Pi1)

ldi2 = f( di2 , 2Pi2' lPi2' 3Pi2' ••• , r Pi2)

ldik = f( dik, lPik' 2Pik' 3Pik' • •• I rPik)

2dil = f( dil , 2Pil' lPil' 3Pil' · .. , rPil)

2di2 = f( di2 , 2Pi2' lPi2' 3Pi2' · .. , r Pi2)

which gives a set of rk simultaneous equations in rk

endogenous variables for each coromodi ty i. Estimation of

these equations, however, poses serious practical problems.

First, data on regional demands are virtually non-existent.

Although regional consumption patterns may be derived

indirectly from production and interregional shipments, the

shipment data themselves are ei ther scarce or irrevocably

14

distorted due to intermediate storage and transshipment. 6

Second, co1linearity among the price variables will most

likely reduce the efficiency of parameter estimates

considerably.

One way to circumvent these problems is to modify the

equations in (1.5) into a form that is compatible with

available data and also more agreeable to the exigencies of

estimation. A simple approach is aggregation of rdik's over

all k's and replacing the price variables by an appropriate

measure of comparative cost. Thus reducing (1.5) to only r

equations and adding transport costs from (1. 4) we will

have:

10 i f( d (Pi -1Pi) L t1k / n = Qi'

20 i f( d (Pi -2Pi) L t2k / n = Qi'

(1. 6)

rOi f( d (Pi -rPi) , L trk / n ) = Qi'

6 For a detailed discussion of problems associated with data on in~erregional flows see Garnick (1980). Adams, Haynes, et al. (1979) have estimated regional demands for lumber and plywood in six u. S. regions for 1950-76. Their method is, however, complex and difficult to replicate. Work on updating the data is presently underway at the Pacific Northwest Forest and Range Experiment station in Portland, Oregon.

15

where rDi = 2: rdik, rPi is the regional price of i as

defined in (1.4) and Pi' as before, is the weighted average

price of the same good in the national market.

Regional product demand relationships in our model

follow the same form as in (1.6), which relates the demand

for a region's output to the total demand for that product

and the region's price competitiveness vis-a-vis the

corresponding price of the same good in the national market.

Note that the coefficients of dQi,s measure the elasticity

of regional output relative to the industry output and the

price elasticities, i.e. the coefficients of the price terms

in parentheses, measure the competitive component of the

regional market shares. 7

Regional Product Supply

Regional product supply functions constitute another

essential ingredient in our model. As we have already noted,

any model of spatial competition pivots on two elements of

locational advantage and local prices. If a region lowers

7 This coefficient is conceptually analogous to the "elastici ty of import substi tution" , the measurement of which has been the subject of perennial interest --and controversy-- in the international trade literature (Tinbergen 1946, Polak 1950, Ginsburg and stern 1965). Several alternative formulations of the relationship between the two price terms have been suggested in the lierature. Two formulations that immediately come to mind are: a) to cast the relationship in ratio form, i.e., ( p /p ), or b) presentation of the two prices separately in theie~ation. These possibilities will be explored further as we proceed to develop the exact estimating equations in the following sections.

16

(raises) its price, the quantity demanded of its product

will increase (decrease) due to the fact that other regions

will sell less (more). The regional differences in price

depend largely on relative elasticities of supply. The point

is demonstrated graphically in Figure (1). The figure shows

the market& for a homogeneous product in two regions a and

b. Both markets are in equilibrium with equal market shares

(Qlto = Q2tO)· The demand schedules Dto are sloped smoothly

because due to the aforementioned "regional sUbstitution

effect" are expected to be more elastic than the industry

demand (Engle 1979a). Sa and Sb are the supply schedules in

the two regions. The only difference between the two markets

is that the slopes of supply curves are not the same.

p p

I I I I Q Q

(a) QltO (b) Q1t1 Q2t1

Figure 1. Effects of alternative assumptions regarding elasticities of supply.

Suppose that the demand schedule shifts from Dto to

Dt1 • The subsequent resul ts of the shift and its

implications in terms of output and market share clearly are

not the same for the two regions. This differential impact

is quite evident in the difference between (QltO-Qltl) and

17

(Q2tO-Q2tl) which has resulted from unequal elasticities of

supply in the two regions.

Supply functions are often much more diverse in nature

than demand functions. They are derived in a fashion

analogous to consumer utility maximization, that is,

maximization of output by the producer subj ect to certain

cost considerations (although this is not the only mode of

optimizing behavior for the producer). Supply functions, as

distinct from production functions that relate quantities of

output to various inputs, describe the response of output to

price, factor costs and other technological, institutional,

or ecological factors (Labys 1973, ch.3). In the most

general case a supply function may therefore be specified in

the following form:

(1. 7)

where Si is the quanti ty supplied of product i, p. ~

is the

price of i, w. ~

to wn represent various input prices. Note

that all variables carry regional subscripts that have been

omitted for convenience.

Regional Factor Markets

Two factors have so far been identified that determine

a region's market share in the national economy: location

and price of outputs. Since locations are predetermined,

competitiveness of a region is ultimately determined by the

18

level of productivity in its industries and their cost

performance relative to their competitors in other regions.

It is apparent from equation (1.5) above that the level of

output is in part determined by the price of inputs. If

factor supplies are perfectly elastic, then we could assume

their prices as fixed and need not worry about what goes on

in the local factor markets. However, in reality (and

consistent with economic theory), returns to a factor of

production are market determined, i.e, in equilibrium they

can be represented as the intersection of demand for and

supply of the factor.

Factor markets are therefore inseparable from the

product market. The key to a better understanding of the

linkages between the two markets is to develop a conceptual

framework in which the relationship between prices in the

two markets can be explicitly defined.

The relationship between product price and input

prices is straight forward and can be derived from

producer's profit maximizing behavior. The producer's total

revenue is determined by the quantity of output (q)

multiplied by the unit market price (p). Producer's profit

is defined as the difference between total revenue and total

cost. Thus in a production process involving two factors,

letting xl and x2 be the levels of input of each factor 1

and 2 with wl and w2 representing their respective unit

prices, we have:

19

(1. 8)

where,

(1. 9)

The producer's demand function for each input can be derived

directly from the profit ;unction by substituting for q from

(1.9) , setting the partial derivatives of the new equation

with respect to xl and x2 equal to zero, and then solving

for xl and x2 • See for example Intriligator (1971, p. 191)

and Henderson and Quandt (1980, p. 80). Thus for a given

production function, the demand for a factor may be

expressed in terms of its own price, the price of other

inputs, and price of output, i.e.:

(1.10) for i=1. •. n

and j=1. •• n-1

This relationship implies that a producer's willing­

ness to pay for factors is essentially constrained by the

price he is able to obtain for his product. Validity of this

conclusion is intuitively clear and consistent with the

derived demand concept.

On the other side of the market are the suppliers of

factors who, very much like all other producers, are also

concerned with getting the most for their lot, that is,

20

maximizing their profit (or present worth as in the case of

natural resource commodities). Their behavior can therefore

be explained within the framework of conventional static

supply theory. In the case of natural resource commodities,

however, the requisite for profit maximization is that the

opportunity cost of holding reserves also be accounted for.

One way of expressing the latter in a form amenable to

empirical estimation is the use of proxies such as total

available stocks or inventory. In our analysis we suggest to

specify the factor supply relationships in the following

form:

(loll)

Where sF i is the quantity supply of factor i in a given

region, wi is the corresponding factor price, xi represents

a measure of available stock of factors or inventory, and X

is a vector of exogenous institutional, or otherwise non­

economic factors.

The complete Hodel

If there are r producing regions, n commodities and m

factors, then relationships (1.2), (1.6), (1. 7), (1.10), and

(loll), constitute a system of 2rn + 2m + 1 equations in

2rn + 2m + 1 endogenous variables, namely, rn commodity

prices (Pi)' rn regional

(Wi)' m regional factor

supplies (Si)' m factor prices

supplies (SFi ) , and 0i. For

21

convenience and ease of reference the complete system of

equations developed so far is rewritten belotor :

Aggregate Demand: dQ . l. = f( Pi' p. ,

J Z )

Demand for Regional Products: D. f( d (Pi-rPi)' = Q. , r l. l.

I trk In )

Regional Product Supplies: rSi = f( Pi' wI·· .wn '

Regional Mkt. Equilibrium: rDi = rSi

Regional Factor Demands: dF~ = f( wi' wj , p. ) .... l.

Regional Factor Supplies: sF. = f( wi' Xi' X ) l.

The major elements and interactions of the model are

given in Figure 2, which shows a schematic outline of the

model structure. In addition to the behavioral relationships

discussed above, the influence of imports on the product

market and the impact of institutional factors on regional

factor markets are also recognized.

The model developed here is intended to serve as a

general framework for the analysis of interregional

competition. In the jargon of econometric model building our

approach here is commonly described as top-down modelling,

as distinguished from the bottom-up approach (see Ballard,

Glickman, and Gustely 1980; also Milne, Adams, and Glickman

1980). The model relies on the national economy to determine

the overall level of sectoral activity which is then

allocated across producing regions on the basis of their

relative costs and locational characteristics. Our proposed

22

formulation, however, departs from a purely top-down

structure in that it allows for feed-backs from regional

economies through price variables.

Exogenous .. Aggregate Variables Prod. Demand

t Imports ~ NatIonal Mkt. .... po Price

+ It , .. ~egional Prod. .... ... !Regional Prod. ... Demand for

Supply .... .. Prices ... .. lRegional output

+ 1

Regl.onal Regional ~ ~ Regional Factor Demand .. Factor Prices .... .. Factor Supply

I ·t IInstitutl.onal Inventory Constraints

Figure 2. Model flow schematic

Before we proceed with the application of this model

to actual data, the commodity dimension of the model must be

fully developed. Therefore, this model can only serve as a

prototype in the most general sense of the term. Further­

more, all relationships have been presented in their static

forms. From an empirical point of view, no conclusions can

be reached with regards to the appropriate functional forms

or adjustment processes before the nature of the commodity

under investigation is fully understood. A thorough

23

discussion of these issues will be undertaken in the

following sections where we will apply the model to the

analysis of interregional competition in the wood products

industry in the united states.

CHAPTER II

THE INDUSTRY

The choice of the softwood forest products industry

for the present study was motivated by the industry's

several characteristics that render it suitable for the

analysis of interregional competition. First, it is an

important industry. In 1984, the lumber and wood products

industry accounted for nearly four percent of total employ­

ment, and three percent of value added in manufacturing in

the United states. The industry's contributions in terms of

employment and income are particularly pronounced at the

local and regional levels. In states such as Oregon and

Washington, for example, respectively forty and close to

twenty percent of manufacturing employment originates in the

timber related activities. 1

Second, it is a highly competitive industry character­

ized by a very large number of firms with relatively low

1 The Pacific Northwest states rank highest in their dependence on the forest products industries. In other major producing regions such as the South, local economies are much more diversified. Among the Southern states, Arkansas, where the forest products industries account for slightly over sixteen percent of basic employment, is the most timber dependent state in the region (Scha11au and Maki, 1986).

25

levels of concentration. In 1984, for example, there were

over thirty thousand firms in the industry nationwide.

Third, the industry is also highly localized:

roundwood is heavy, bulky, and the manufacturing processes

for most products entail considerable losses in weight, as

well as, in volume. The manufacturing facilities are,

therefore, invariably located near the sources of timber

supply concentrated in few distinct regions in the country.

The forth and final factor in selecting this industry is

product homogeneity; a condition (assumption) that is

central to the analysis of interregional competition.

certain differences in grades and species notwithstanding,

the main products of the industry such as lumber, plywood,

and pulp, are sufficiently similar with respect to specific

end uses to be considered homogenous.

THE STRUCTURE OF THE INDUSTRY

The softwood forest products industry is a complex and

multi-faceted system that encompasses a wide range of

activities extending from forest lands to the consumption of

final products. This system is shaped and regulated by the

confluence of many economic, biological, institutional, and

spatial factors.

Broadly defined, the industry consists of wide a range

of activities in which timber, in combination with other

inputs (capital, labor, energy, etc.), is used to produce a

myriad of consumer products. The most commonly accepted

26

classification of these products is in terms of the stage of

processing, and involves two categories of primary and

secondary products. The main processing stages and maj or

primary products of the forest products industry are shown

in Figure 3.

Growing stock

I .. Roundwood

1 . + Ml.sc.Products

+

+ Fuelwood ~

.. Residue

+ Sawlogs Veneerlog Pulpwood

I Woodpulp ..-__ ----.1.

+ Lumber Plywood Paper

Figure 3. Major products and stages in processing of timber.

Roundwood products, which are used primarily in the

production of lumber, pulp, and plywood, claim the largest

portion of annual removals of timber in the united states.

Forest Service estimates show that during the 1970's, nearly

95 percent of annual harvest of softwood timber was in the

form of roundwood. Miscellaneous products such as poles,

pilings, posts, mine timber, etc., accounted for an

additional 2.5 percent; and the remaining 2.5 percent was

divided in near equal proportions between fuelwood and

residual products. (USDA/Forest Service, 1982).

27

The present study focuses on two of the primary forest

products: softwood lumber and plywood. These products are

two of the most important outputs of the forest products

industry in the U. S. and together account for about 70

percent of annual consumption of softwood timber in the

country.

THE MARKET PROCESS

In a free market, "industrial competition" is defined

in part as a condition wherein every productive resource in

an industry "earns as much, but no more than, it would in

other industries" (Stigler, 1968, p. 10). This condition

holds because the profit maximizing behavior of owners

guarantees that resources are employed where they obtain the

highest returns. Timber is a versatile raw material which is

used in the production of a wide range of products. At any

given time, the producers' economic considerations, 1. e.

profits, determine the type of product into which timber is

likely to be transformed.

The level of output for each product is in turn

determined by market conditions. Producers supply what

consumers

mechanism.

quantities

demand of them. Prices are the equilibrating

For each product, market clearing prices and

are dictated jointly by consumer demand and

supply conditions.

Demand: Softwood lumber and plywood are producer

goods. Demand for these products is, therefore, a derived

28

demand and depends largely on the level of activity in their

respective end use markets. The principal end uses for

softwood lumber and plywood and levels of demand in each

market in selected years are shown in TABLE I.

TABLE I

DOMESTIC LUMBER CONSUMPTION BY END USE CATEGORY (PERCENT OF TOTAL CONSUMPTION)

Lumber 19521 19844

Residential construction ••• : 36.7

Non-residential construction ••• : 18.7

Repair and alterations •••• : 16.5

Material handling and shipping ••• : 16.0

Manufacturing and other •••••• : 12.0

Plywood

Construction •••• : Manufacturing

and other •••••• :

51.0

49.0

45.4

9.90

15.2

14.1

12.8

55.4

44.6

34.1 38.1 38.8

10.2 10.5 15.4

13.0 13.3 26.3

15.8 16.1 10.0

12.9 10.1 9.50

59.1 65.7

40.9 34.3 31.0

1- SRI (1954); 2- USDA/Forest Service (1973); 3- USDA/ Forest Service (1982); 4- wes~ern Wood Products Assoc. (1984); 5- Am. Plywood Assoc.

2 It is important to note that the data on consumption patterns are based on estimates derived from different sources. In several instances comparison of data across various sources show considerable discrepencies. For example in a 1982 survey of lumber use in non-residential construc­tion (Spelter and Anderson, 1985) lumber consumption in this market is estimated at around seven percent of total domestic consumption.

29

Historically, the construction industry has been the

single most important source of demand for softwood lumber

and plywood. As figures in Table I indicate, since 1950, the

construction sector has accounted for an average of 70

percent of all softwood lumber and 60 percent of all

softwood plywood consumed in the united states. Witi.lin the

construction industry, new residential construction is

responsible for the largest portion of lumber and plywood

consumed in this sector.

other major uses of lumber and plywood are in shipping

and manufacturing (mostly wood furniture). During the past

three decades, the use of lumber and plywood in these

activities has followed a continuously declining trend. The

declining role of timber products in activities other than

construction is particularly evident in the historical

pattern of plywood consumption.

Supply: Levels of output in a competitive industry are

determined by the producers' ability to respond to changing

demand and factor supply conditions. In order to succeed in

a competitive environment, the industry has to continuously

improve its productivity so as to decrease its production

costs subject to technological constraints inherent in its

production process.

The production of lumber and plywood is each comprised

of a series of operations in which roundwood is converted

into the final product. These operations are summarized in

Table II. During the time period covered in the present

30

analysis, most of these operations have undergone consider­

able technological change.

TABLE II

LL~BER AND PLYWOOD PRODUCTION PROCESSES

Lumber

1) Log handling 2) Breakdown 3) pipping & Trimming 4) Crosscutting 5) Drying 6) Surfacing

Plywood

Log handling Peeling or Slicing Drying Assembly lay-up Glueing Finishing

Technological improvements in the wood products

industry have been char~cterized by Heady (1952) as being

either "biological", or "mechanical". According to this

classification biological innovations are essentially of the

"neutral" type and tend to increase the marginal output of

all inputs without altering their sUbstitution properties.

Improvements in plant lay-out, enhanced waste utilization

techniques, and the use of thinner saw kerfs are all but few

examples of this type of technical progress. Mechanical

innovations, on the other hand, are resource saving changes

that raise the marginal product of specific inputs relative

to others. Some examples of the latter type of technical

change are mechanized log handling techniques, computerized

log scanning methods, and improvements in small-log peeling

technology in veneer production.

31

The structure of production in the lumber and wood

products industry has been analyzed in several recent

studies including those by Robinson (1975), Humphrey and

Moroney (1975), Alperovich (1980), stier (1980), Merrifield

and Haynes (1983, 1984), and Nautiyal and Singh (1985). With

the exception of Alperovich (1980), and Merrifield and

Haynes studies of the Pacific Northwest forest products

industry, these studies generally involve analysis of broad

product categories at the aggregate national level. There is

therefore little information on patterns of technical change

associated with specific products in various regions.

since these studies have employed different production

functions and involve different product categories, their

results are not always directly comparable. They do,

however, reach some general, though important, conclusions

that bear directly on our analysis. The first conclusion is

that the rate of technical progress and productivity gains

in the lumber and wood products industry has at least

paralelled those of other manufacturing industries in the

country. Second, due to rapid increases in labor and

stumpage costs, the trend in technological change has tended

towards labor --and to a lesser extent stumpage-- augmenting

improvements. Third, most factor inputs in the industry are

substitutable; and, that sUbstitution possibilities between

capi tal and labor, and capital and stumpage, are greater

than those of other inputs.

32

with respect to scale effects, however, the results of

these studies remain by and large inconclusive. Merrifield

and Haynes (1984), for instance, find no evidence of scale

effects in the industry; while Robinson (1975) concludes

that gains in productivity have been largely attributable to

economies of scale.

THE SPATIAL DIMENSION

The market processes disscussed in the preceeding

section determine the quantity and type of product that is

likely to be produced at any given point in time. In an

industry characterized by a geographically fragmented

market, the very same forces also decide "where" each

product will be produced.

In the softwood products economy, this locational

dimension arises because of the spatial imbalance of supply

and demand resulting from an uneven distribution of

producers and consumers of forest products throughout the

united states. Historically, the consumers of forest

products have been concentrated in the Northern states,

while major sources of timber supply and production

facilities are located in the South and the west.

The two sets of supply and demand areas, together with

the transportation costs that connect them, constitute a

dynamic system. The supply regions compete with one another

to market their products in supply areas. Prices are again

the equilibrating mechanisms. If demand for a region's

33

product is excessive relative to production possibilities,

the price in that region will rise leading demand to shift

to other producing regions. This will in turn lead prices in

the initial region to fall until a new equilibrium is

reached.

In the present study, this spatial dimension is

represented by partitioning the continental united states

into a set of contiguous regions. Five domestic lumber

supply regions (Pacific Northwest, South, Southwest,

Inland, and North), two plywood supply regions (NW and SO),

and six product demand regions are considered. See Figures 4

and 5. Lumber output from the North region is treated as

exogenous. Product supplies from Alaska and Hawaii are not

included because their contributions to the domestic market

are small; and regional exports of plywood are ignored.

The main factor underlying the development of this

spatial framework' was the practical considerations of data

availability. A basic consideration in specification of

supply regions was that activities and product types should

possess some degree of homogeneity. The supply region

bounda~ies specified here correspond closely with the Forest

service Administrative Regions and are essentially identical

to supply areas considered in the Timber Assessment Market

Model (Adams and Haynes 1980). The choice of demand regions

was determined entirely by the availability of transport

costs data.

34

Figure 4. Product supply regions.

Figure 5. Product demand regions.

35

REGIONAL MARKET SHARES

Market shares are here defined as the percentage of

total domestic demand supplied by a producing region. Total

demand on producers in a supply region (regional production)

is determined by combining market shares wi th exports to

other countries.

Tables II and III present market share data covering

the 1950-1984 period for softwood lumber and plywood

produced in various supply regions. Examination of the these

historical trends in market shares reveals that significant

changes in distribution of production across various regions

has taken place.

Pacific Northwest: The main lumber products of this

region come from Douglas Fir which is especially prized for

its structural properties. Until 1965, the Pacific Northwest

enjoyed a relatively stable position in the domestic

softwood lumber market, producing annually about one third

of total softwood lumber consumed in the country. Since

then, save minor increases in 1974 and 1975, the region's

market share has declined steadily (see Figure 6).

Data on shipments of lumber from the Northwest show

that the region's loss in market share in recent years can

be primarily attributed to losses in the Northeast and

Northcentral markets. Rapid rises in transport costs

combined with increases in stumpage prices in the Northwest

have placed the region in great disadvantage vis-a-vis other

36

TABLE III

REGIONAL LUMBER MARKET SHARES (% OF TOTAL CONSUMPTION)

Market Shares Consumption

(MMMBFt. ) NW SO SW IL NO CAN Year 1950 33.4 34.7 30.6 12.6 7.3 5.5 8.7 1951 30.9 36.4 28.1 15.4 7.0 5.9 6.7 1952 31.9 38.5 27.9 14.0 7.7 4.9 6.7 1953 31.6 37.5 25.1 15.9 8.2 5.4 7.6 1954 31.6 36.5 24.7 16.0 9.2 4.7 8.7 1955 32.5 36.7 24.0 16.1 9.2 4.0 9.9 1956 32.7 32.6 25.4 17.7 10.7 4.1 9.4 1957 29.2 33.3 23.5 18.1 10.3 5.7 9.1 1958 30.0 35.7 21.5 17.4 10.9 4.1 10.3 1959 33.6 34.6 21.3 17.7 11.5 3.9 10.9 1960 29.6 36.0 19.8 17.0 11.0 4.0 12.1 1961 29.4 34.8 19.6 16.8 11. 3 4.0 13.4 1962 30.7 35.1 19.2 16.0 11.4 3.7 14.7 1963 31.7 34.4 19.3 15.5 11.4 3.9 15.7 1964 33.3 35.4 19.6 15.3 12.0 3.2 14.6 1965 33.3 35.2 20.2 14.8 12.2 3.1 14.6 1966 32.6 34.4 20.4 15.0 12.5 3.3 14.5 1967 31.8 33.9 20.7 14.9 13.0 3.2 14.9 1968 34.8 33.0 20.0 15.2 12.8 3.2 16.5 1969 32.9 29.2 22.2 15.4 13.3 3.2 17.6 1970 31.6 29.1 21.8 15.8 12.9 3.2 18.1 1971 36.0 29.0 21.8 14.8 12.3 2.8 19.9 1972 38.4 28.1 20.8 14.6 11.4 2.6 23.1 1973 38.4 28.2 20.6 14.6 11.6 2.9 23.0 1974 33.2 31.2 21.0 13.6 11.4 3.3 20.3 1975 30.2 29.3 23.1 13.5 12.7 3.6 18.8 1976 36.4 28.0 21.7 13.0 12.3 4.3 21.8 1977 40.8 26.4 21.6 12.1 11.4 4.1 25.3 1978 42.8 25.4 21.6 11.1 10.4 4.4 27.5 1979 41.0 24.9 22.7 11.0 10.0 4.6 27.1 1980 34.5 23.2 23.8 10.6 9.9 5.1 27.7 1981 32.1 23.4 26.4 9.7 9.7 3.5 28.7 1982 31.4 22.1 27.9 9.2 8.8 3.4 29.0 1983 41.5 22.9 24.6 8.9 10.2 3.1 28.8 1984 43.0 23.4 24.7 8.9 9.4 3.0 30.8

Source: Adams, Jackson, and Haynes (1986); Western Wood Products Association statistical Yearbook.

37

producing regions, leading to significant encroachments on

this region's share of the Northern market.

Recent trends in lumber production in the Northwest

do, however, suggest that the region's market shares during

the 1980's have been somewhat stable, fluctuating around a

historical low level of about 23 percent.

The South: The historical trend in lumber production

and market shares for the South are markedly different from

what we have observed in the Northwest. During the decade of

50's, lumber production in the South declined steadily

resulting, on the average, in an annual loss of about one

percent in market shares. After a relatively long period of

stability in the sixties and the greater part of the

seventies, however, the region's market shares began to rise

considerably. In 1983 lumber production in the South reached

an historically high level of 10.5 billion BFt. and rose to

near 11 billion BFt. in 1984.

The Southern region covers a significantly large

territory and, unlike the Northwest, the largest segment of

its market consists of intra-regional shipments. The most

significant change in market shares of the Southern lumber

in recent years was associated with the region's performance

in 1981 and 1982. During these years, the market share of

Southern producers increased by nearly 2.5 points per year.

The performance of the South in the plywood market has

been much more astounding. During the past three decades,

plywood consumption in the Uni ted States has grown

38

consistently at an average rate of near 500 million square

feet per year. Prior to 1964 virtually no plywood was

produced in the South. In this period, the Northwest

producers, located mostly in the Coastal region, comfortably

commanded near 90 percent of the domestic plywood market.

Refinements in small-log peeling technology during the

1960's, induced by the rapid growth in plywood demand,

provided the grounds for the development, and subsequent

expansion, of the industry in the South. Production figures

for the Southern plywood show that since 1965 the South has

not only absorbed nearly all increases in domestic demand

for softwood plywood, but indeed has encroached significant­

lyon the Northwest's market shares.

Market share figures for the two regions show that the

Northwest entered the 1970's with a market share of almost

three times that of the South (see Figure 7). Currently,

South's market share stands 11 points above the Northwest.

Southwest: Softwood lumber production in the SW has

remained at a more or less steady level of approximately 4.5

billion BFt. a year. During the 1950's and 1960's, the

species composition of lumber produced in the region

--consisting of large quantities of redwood-- allowed it to

maintain a relatively stable share in the domestic market.

In recent years, however, decl ines in redwood production

have made it more and more difficult for the region to keep

pace wi th increases in domestic demand, leading to

sUbstantial losses in market shares.

39

TABLE IV

REGIONAL PLYWOOD MARKET SHARES (% OF TOTAL CONSUMPTION)

Market Shares Consumption (MMSq. Ft.) NW SO SW IL

Year 1950 2554.00 93.10 0.00 6.90 0.00 1951 2867.10 91.60 0.00 8.40 0.00 1952 3050.00 88.70 0.00 11.30 0.00 1953 3671. 00 88.20 0.00 11.80 0.00 1954 3903.60 87.40 0.00 12.60 0.00 1955 5075.00 87.40 0.00 12.60 0.00 1956 5239.20 86.80 0.00 13.00 0.30 1957 5459.50 86.90 0.00 12.90 0.20 1958 6340.30 87.20 0.00 12.60 0.20 1959 7827.80 85.40 0.00 14.00 0.60 1960 7815.60 84.40 0.00 14.60 1. 00 1961 8576.60 84.20 0.00 13.70 2.10 1962 9513.10 84.80 0.00 12.70 2.50 1963 10216.00 84.30 0.00 12.20 3.50 1964 11678.40 83.90 0.70 11.20 4.20 1965 12447.00 81.00 3.20 9.90 5.90 1966 13056.00 75.70 8.70 8.70 6.80 1967 12958.40 71.30 13.50 6.80 8.20 1968 14694.60 70.50 15.80 6.10 7.20 1969 13694.00 66.00 20.60 6.30 6.70 1970 14340.00 64.80 22.80 5.80 6.20 1971 16634.90 61.40 26.10 5.90 6.10 1972 18324.00 59.40 28.70 5.70 5.80 1973 18305.20 58.70 30.10 5.30 5.60 1974 15877.00 56.10 32.00 5.30 6.30 1975 16050.00 53.90 35.00 4.00 6.70 1976 18440.00 53.20 36.70 3.30 6.60 1977 19376.00 52.20 38.10 2.80 6.50 1978 19964.00 51.60 39.30 2.60 6.20 1979 19653.00 49.10 42.10 2.40 6.10 1980 16311.60 46.10 45.00 2.00 6.70 1981 16731.40 41.50 49.30 2.10 6.80 1982 15805.40 39.70 53.30 1.20 5.50 1983 19525.60 41. 70 50.70 1.30 5.90 1984 19901. 80 41.80 52.00 1. 30 4.40

Source: Adams, Jackson, and Haynes (1986).

40

100,----------------- --------------------------~

90 Canada

so ~North

70

Inland so

SO'Jthwest 50

South

JO

20

Northwest 10

Ig5019521954195819581g8019.2'8&41ge81868'8701872'9741978,9781980,9821984

Figure 6. Regional market shares in lumber as percent of apparent consumption (1950-84). Source: Table III.

100 I n I clnd

Southwest 90

eo

70

so J I

South

50

40

30

Northwest 20

10

0 '.50,852'854,958,958,980'982'184,181,111,.70,.72,,74,978,878,980198219&4

Figure 7. Regional Plywood market shares as percent of apparent consumption (1950-84). Source: Table IV.

41

Inland: Most lumber produced in this region comes

from the Northern Rocky Mountains part of the region. Minor

fluctuations notwithstanding, Inland's share of the domestic

lumber market has remained relatively flat since the early

1950's. Lumber production figures for the Inland region

suggest that changes in regional output correspond somewhat

closely with fluctuations in demand for lumber at the

national level leaving region's market shares unaffected.

Canadian Imports: The United states is the largest

single market for the Canadian softwood lumber (Figure 8).

Indeed Canadian exports to th~ U.s. constitute the largest

flow in international lumber trade (Lindell, 1979).

Imports of lumber from Canada have expanded

continuously since 1950. This expansion has brought about

21 20 111 111 17 HI 15 14 13 12 II 10 II II 7

II

5 4

:5 2 1

o v

'J p: 1\ f\

f\

v v

i% ~~ ~ 1\ 1\ f\ 1\ r, . ,

v V ~I V v VVv

.~

17: ~ ~ ~

~ l% I%~ f\

1\ I'

~" t

U' 'i ~ ~ ~ r, 1\

1\ h .1\ r-

v v

V l/ . V 'V

' .. 'V . ~' . V ~/ V V v'V

11I50III~2111!54111!5SIIl!5llIIlS01I1S211154111651115111111011112111141111511111111111018112111114

IZZl C<lnlumptlon lSSI Exp. 10 u.s, ~ Other Exp.

Figure 8. Canadian lumber production, consumption, and exports. Source: Adams, Jackson, and Haynes (1986).

42

equal, but opposite, changes in market shares of domestic

producers particularly in the West. Traditionally, imports

from Canada have served a market clearing function

fluctuating with changes in demand in the domestic market.

In recent years, however, these imports have exhibited a

behavior suggestive of an increasingly competitive

displacement of domestic production.

The increase in Canadian imports in recent years and

the strengthening of i ts competitive position are often

attributed to declines in the value of the Canadian dollar

in relation to u.s. currency. However, as Adams and Haynes

(l980a) have demonstrated, an equally important factor has

been the production conditions in Canada characterized by

low production costs and elastic supply.

REGIONAL TIMBER RESOURCES

A fundamental consideration in the analysis of the

spatial patterns of production in the wood products industry

is the geographical distribution of timber resources and

variations in supply behavior that arise from differences in

economic objectives and management practices across

ownership categories.

The continental united states contains about 470

million acres of timberland with an additional 12 million

acres in Alaska and Hawaii, which together constitute around

22 per cent of the total land area in the country.

43

Timberlands, as listed in Table V, are categorized by

region and type of ownership. The rows in Table V show the

distribution of timberlands within each region by ownership

type. Four types of ownership are recognized: "National

Forests" , "other public", "forest industry", and "other

private". "National Forests" designates commercial

forestlands that are owned by the Federal Government and

come under the jurisdiction of the Forest Service

(Department of Agriculture). National forests are chiefly

concentrated in the western regions where they consti tute

nearly 53 percent of all timberlands in the region.

The "other public" category includes Federal lands

other than National Forests (primarily lands administered by

the Bureau of Land Management, Department of the Interior),

Bureau of Indian Affairs; and state, county, and municipal

forests. Much of the latter holdings (over 50 percent) are

in the Lake States and consist of lands reverted to local

governments as a result of tax delinquencies during the

30 I s. The BLM lands are primarily located in the Pacific

Northwest (4.1 MM acres) and the Rocky Mountain (1.7 MM

acres) regions.

The "forest industry group", Le., integrated firms

that engage in both growing and processing of timber, holds

approximately 15 percent of total timberlands. The remaining

59 percent (277 MM acres) of timberlands in the continental

united states are owned by farmer and other private

44

entrepreneurs who grow and sell timber but in general~. are

not involved in wood processing. These holdings, which

constitute the largest single ownership class, are by and

large concentrated in the North and the South regions where

70 . 8 and 71. 3 , respectively, of timberlands fall in this

category.

TABLE V

DISTRIBUTION OF TIMBERLANDS BY REGION AND OWNERSHIP IN 1977

(MM ACRES)

National Other Forest Other Total Region Forests Public Industry Private % Total

N.W. 16.83 7.52 9.87 7.97 42.19 % 39.9 17.8 23.4 18.9 9.7

Inland: 36.43 6.73 2.09 12.50 57.75 % 63.0 11.6 3.7 21.7 12.2

P.S.W. : 8.17 0.50 2.68 4.94 16.29 % 50.2 3.1 16.4 30.3 3.5

North 9.83 20.69 17.91 117.71 166.14 % 5.9 12.5 10.8 70.8 35.3

South 10.95 6.78 36.24 134.08 188.05 % 5.8 3.6 19.3 71.3 40.0

Total 82.21 42.22 68.79 277.20 470.42 % 17.5 9.0 14.6 58.9 100

Note: totals do not include Alaska and Hawaii. Source: USDA Forest Service (1982), Appendix 3, 344-9.

Distribution of timberlands is an important indicator

of where timber will be produced in the future. From the

standpoint of the near term supply of wood products,

however, supply sources will be determined by the location

45

of existing inventories of mature timber (Dowdle and Henke,

1985 p. 80).

The quantities of timber supply from these sources are

in turn influenced by biological determinants such as land

quality, growth rates, and type of species; and specific

economic objectives pursued by owners in each region.

Attention here will be focused on two general ownership

categories of "public" and "private". These categories

represent the two timber supply sectors for which management

objectves are distinctly defined.

Timber Supply: Private. The economic theory of timber

supply concerns two central issues of when to harvest and

how much to harvest. The problem of when to harvest (optimal

rotation) may be viewed as a special instance in the

classical theory of capital (Hyde, 1980, pp. 60). The profit

maximizing solution to this problem can be derived directly

from the owner's profit function. Under the condition of

perfect competition, and assuming economic rationality,

timber owners choose harvesting schedules that maximize the

present discounted va1~e of their holdings.

In terms of a fixed land-base with an even-aged stock

of timber, the optimality condition implies that trees

should be cut when the discounted marginal product of the

timber stand (annual growth rates) equals the marginal cost

of withholding the timber for an addi tional year. These

costs consist of the interest on the revenues from the cut,

46

value of silvicultural efforts and, as Samuelson (1976) has

pointed out, the rent on the forest land. 3

Economic theories of optimum harvest provide a useful

framework for the analysis of timber supply in the long-run.

Their utility in explaining actual output levels in the

short-run, however, is 1 imi ted. A maj or impediment in the

application of these theories to short-term analysis is the

predominance of noneconomic objectives for private owners

such as tax considerations and the immediate nature of

cash-flow needs. These issues will be considered in greater

detail in the next chapter as we develop empirically

testable relationships for our model.

Timber supply: Public. Conventional economic tools of

price theory (supply and demand analysis) provide an ample

framework for the analysis of timber supply. These economic

considerations will, however, be of limited use in

explaining supply behavior where significant areas of

commercial forestlands are owned, managed, or in one form or

another regulated by public policy. The reason is that in

such cases an entirely different set of administrative

considerations, which are themselves based on biological or

3 For a thourough theoretical treatment of economic issues concerning timber production see Hyde (1980) particularly Chapter 4. A complete mathematical derivation of the optimality condition can be found in Johansson and Lofgren (1985) Chapters 4 and 6.

47

otherwise "non-economic" functions, dominate the amount of

timber made available to the market.

During the course of this century public policy has

become an increasingly important force in the timber market

in the united states. Indeed, as Deacon and Johnson (1985)

have observed, no other natural resource industry has ever

been as heavily influenced by government ownership and

policy as the timber industry. In 1977, the latest year for

which data is available, public ownership accounted for 28.1

percent (135.7 million acres) of the total timberland in the

country (482.5 million acres). Timber production patterns,

at the same time, indicate that in all parts of the country,

particularly in the west, producers of wood products have

become increasingly dependent on timber supplies from public

lands (see Table VI).

Broadly defined, public timber policy encompasses a

wide range of issues concerning management practices,

marketing procedures and harvesting patterns of timber from

publicly owned forests, taxation of private holdings, and

other regulatory policies at the federal and local govern­

ment levels. These issues, in particular practices concern­

ing the management of the National Forests by the Federal

Government, have been the subj ect of a perennial debate

between economists on the one hand, and environmentalists

and professional forestry experts on the other. A sUbstanti­

al body of research has now been accumulated by either camp

TABLE VI

ANNUAL HARVEST OF SOFTWOOD TIMBER BY REGION AND OWNERSHIP (1950-1984)

----------------------------------------------------------------------------------------------------Northwest South Southwest Inland

---------------------- ---------------------- ---------------------- ----------------------Year Total Public Private Total Public Private Total Public Private Total Public Private

(MMCFt. ) " " (HMCFt. ) , " (HMCFt. ) "

, (MMCFt. ) " % 1950 2501.7 22.4 77.6 3424.1 6.1 93.9 731.0 15.0 85.0 537.1 49.8 50.2 1955 2826.0 28.5 71.5 3165.2 7~4 92.6 933.3 21.3 78.7 662.3 71.3 28.7 1960 2744.2 34.8 65.2 2770.4 9.4 90.6 926.6 28.5 71.5 672.6 67.9 32.1 1961 2689.5 37.6 62.4 2697.3 8.8 91.2 915.8 29.9 70.1 687.6 70.3 29.7 1962 2850.6 41.1 58.9 2726.3 9.2 90.8 905.2 30.5 69.5 734.2 72.4 27.6 1963 2957.5 44.8 55.2 2795.8 9.0 91.0 913.2 36.2 63.8 787.0 77.4 22.6 1964 3173.7 45.7 54.3 2981. 3 8.5 91.5 945.0 39.3 60.7 835.1 72.6 27.4 1965 3254.0 45.9 54.1 3121. 3 9.0 91.0 909.8 41.5 58.5 872.8 74.0 26.0 1966 3162.5 42.0 58.0 3240.9 8.3 91.7 903.2 42.9 57.1 896.4 75.5 24.5 1967 3083.4 41. 6 58.4 3243.5 8.4 91.6 855.8 44.2 55.8 893.6 72.2 27.8 1968 3349.7 44.3 55.7 3438.4 8.0 92.0 973.5 48.4 51.6 947.3 75.9 24.1 1969 3099.3 45.0 55.0 3684.7 8.0 92.0 925.8 43.1 56.9 914.6 77.5 22.5 1970 3077.5 37.9 62.1 3690.8 7.6 92.4 904.5 41.2 58.8 831.6 72.0 28.0 1971 3057.6 42.7 57.3 3747.8 7.8 92.2 910.3 45.7 54.3 856.7 71. 5 28.5 1972 3239.3 48.6 51.4 3918.1 8.4 91.6 959.6 46.7 53.3 845.9 69.2 30.8 1973 3275.9 48.5 51.5 3918.8 7.1 92.9 963.5 42.9 57.1 848.4 66.2 33.8 1974 3006.5 41.8 58.2 3829.3 7.9 92.1 778.5 45.3 54.7 749.9 68.0 32.0 1975 2682.1 38.9 61.1 3636.1 9.2 90.8 701.1 44.3 55.7 762.3 60.0 40.0 1976 3113.6 41.7 58.3 3982.4 9.7 90.3 803.7 47.7 52.3 849.6 64.9 35.1 1977 3050.3 40.7 59.3 4218.4 8.7 91.3 820.1 44.9 55.1 873.2 60.5 39.5 1978 3098.5 43.2 56.8 4444.7 9.1 90.9 785.5 46.9 53.1 854.0 58.5 41.5 1979 3046.2 43.6 56.4 4675.2 8.4 91. 6 747.6 47.6 52.4 860.6 58.8 41.2 1980 2673.7 38.8 61.2 4659.2 9.3 90.7 608.1 51.9 48.1 774.7 55.1 44.9 1981 2306.6 37.4 62.6 4770.4 8.7 91.3 526.4 45.2 54.8 715.6 60.1 39.9 1982 2327.3 28.8 71.2 4662.2 7.6 92.4 477.3 44.0 56.0 664.0 50.8 49.2 1983 2727.9 42.2 57.8 2601. 8 17.7 82.3 581. 6 60.4 39.6 681.1 79.7 20.3 1984 2805.3 45.8 54.2 3067.3 15.2 84.8 637.3 51.8 48.2 725.6 71.4 28.6 ----------------------------------------------------------------------------------------------------Source: Appendix A, [1] I [19].

~ OJ

49

in support of its position. 4 Much of this controversy

centers on two principles that have dominated the management

of National Forests in the country over the past two and

half decades: "sustainable yield" and "multiple use", both

embodied in the Multiple-Use sustained-Yield Act of 1960.

A central issue in this controversy concerns the

"sustained yield" requirement of the act and the concepts of

"even flow" and "allowable cut", the practical implications

of the mandate. At the core of criticisms concerning public

timber policy in the U.s. lies the issue of economic

efficiency of these principles and their inconsistency with

the economic concept of "supply".

Regional inventories of softwood sawtimber on National

Forests and other ownerships are presented in Table (VII).

A comparison of figures in Tables (V) and (VII) reveals that

distribution of timber resources does not follow the same

pattern as timberlands. Major differences exist in the

intensity of timber stands across regions and among

ownership categories. The most readily discernible pattern

in the distribution of sawtimber is that the volumes of

standing timber on National Forest lands are generally in

4 Deacon and Johnson (1985) provide a collection of most recent studies on the subject of government timber policy. More technical treatments can be found in Hyde (1980) especially Chapters 2 and 7; and Samuelson (1976).

50

excess of the proportion of forest area in all regions,

indicating much higher densities on the average. This latter

observation has, among other things, been cited as an

important indication that National Forests produce less than

their share of domestic timber output (Howe, 1979 pp. 223).

Region

N.W. %

Inland: %

P.S.W. : %

North : %

South %

Total : %

TABLE VII

VOLUME OF SOFTWOOD SAWTIMBER BY REGION AND OWNERSHIP

1977 (MM BFt.)

National Other Forest Other Total Forests Public Industry Private % Total

386623.0 140322.0 141004.0 59537.0 727486.0 53.1 19.3 19.4 8.2 40.4

260758.2 42774.1 23260.4 53586.8 380379.5 68.5 11.2 6.2 14.1 21.1

157958.0 6356.0 40833.0 50397.0 255594.0 61.8 2.5 16.0 19.7 14.1

8049.9 8.3

11942.1 22734.4 53777.1 96503.5 12.4 23.6 55.7 5.5

33979.7 13883.6 86389.7 206769.5 341022.5 10.0 4.0 25.4 60.6 18.9

847368.8 215277.8 314271.5 424067.4 1800985.5 47.0 12.0 17.4 23.6 100

Note: totals do not include Alaska and Hawaii. Source: USDA For. Service (1982), An Analysis of the Timber situation in the United States, Appendix 3, pp. 370-71.

These and other normative issues cOJ'lcerning public

timber policy are important and merit close scrutiny and

detailed analysis. Such undertaking, however, is well beyond

the scope of the present study. Our interest in the area is

51

a purely empirical one: the manner in which such policies

manifest themselves in timber supply behavior of various

regions; and the insight they can provide in modeling this

behavior.

The extent to which timber offerings from public lands

affect regional markets is determined by the relative share

of the public component of total production. In analyzing

the short-run effects of public timber supply on local

stumpage markets, it is essential to distinguish between

"timber offerings" and actual "harvest levels". Timber from

National Forests and other public lands is usually sold

under four-year removal contracts. Quantities of timber

harvested in anyone period thus do not necessarily

correspond with timber offerings in that period. While

market conditions in the long-run are decided by levels of

timber "sold" from public lands, actual short-run harvest

levels are determined by local demand and price levels. In

short-run analysis, therefore, no distinction need be made

between supply sources. Total harvest, consisting of harvest

on both public and private ownerships, can be explained in

terms of conventional supply theory.

CHAPTER III

THE EMPIRICAL MODEL

In Chapter I we outlined a general conceptual

framework for a mu1tiregiona1, multi-industry model and

described its major ingredients and their conceptual

contents. Based on these theoretical considerations and the

insight we have gathered from our discussions of the lumber

and plywood industries and the timber economy in Chapter II,

we are now in a position to proceed with the development of

our industry-specific model. To aid us in the task, is also

the wealth of information provided by previous econometric

analyses of the forest economy, most notable among them, the

pioneering studies by the Stanford Research Institute

(1954), Holland (1960), Gregory (1960), McKillop (1967,

1969), and other more recent works of Adams and Blackwell

(1973), Robinson (1974), Mills and Manthy (1974), Holley,

Haynes, and Kaiser (1975), Adams (1977), and Adams and

Haynes (1980).

A1 though these studies have, by and large, adopted

fundamentally similar specifications in presentation of

individual behavioral relationships, there are marked

differences among them in terms of objectives, scope (the

degree of spatial aggregation and sectoral presentation),

53

and model structure. 1 From a genealogical point of view, our

model is a direct descendant and extension of Adams'multi-

regional, multiproduct model of the U. S • softwood timber

market (Adams 1977) and the Timber Assessment Market Model

developed by Adams and Haynes (1980).

Both studies were designed as forecasting tools for

the long-range projection of activity in the product and

stumpage markets and assessment of potential impacts of

alternative resource use policies in the private and public

timber sectors. In the taxonomy of regional models, Adams'

approach is a combined top-down/bottom-up framework. The

model considers two products (softwood lumber and plywood),

four product supply regions (including Canadian imports) and

three stumpage supply regions (see Figures 4 and 5 in

Chapter II) • Treating regional supplies as perfect

substitutes, equilibrium quantities and aggregate product

prices (at the national level) are then established jointly

by the levels of aggregate demand and regional supplies. The

model ignores transportation costs so that product prices in

the supply regions are identically the same as the demand

price at the national level.

Timber Assessment Market Model (TAMM) , on the other

hand, is a purely bottom-up model. It is by far the most

1 For a comprehensive survey of econometric studies of the forest economy see Adams and Haynes (1980). A bibliography of earlier projection studies can be found in Gregory, et al. (1971).

54

comprehensive modeling effort in the analysis of the timber

economy in the united states. The spatial structure of TAMM

is based on partitioning of the national market into nine

product and stumpage supply regions and six demand regions.

For each supply region equilibrium solutions for product

prices and quantities are found by simultaneous estimation

of the regional product and stumpage relationships. Given

interregional transportation costs in a given period,

equilibrium spatial price and regional outputs are computed

via a programming procedure which utilizes the reduced form

of the regional supply equations and regional demand

relationships in an iterative process to find the profit

optimizing levels of supply in each region.

The most outstanding feature of TAMM that

distinguishes it from most other projection models of the

forest economy, is its explicitly simultaneous treatment of

interdependent market relationships, specifically, the

linkage between regional stumpage and product sectors which

allows simultaneous determination of market clearing prices

in both markets. For a complete description of the model

structure and interactions of TAMM the reader is referred to

Adams and Haynes (1986).

The model developed in the present study incorporates

and combines features of the two models we have described.

It is, however, designed for the purpose of short term (one

to two year) forecasting. Certain long-run consideraticns

55

such as regional production capacity adjustment nlechanisms

are ignored and resource availability takes on either a

simplified form, or in some cases, is ignored completely.

THE MODEL, ITS STRUCTURE, AND COMPONENTS

The model, as described in Part One, contains three

interrelated components: 1) the national product market, 2)

regional product market, and 3) the regional factor market.

Due to exigencies of estimation, certain modifications

of the initial conceptual model were deemed necessary

without compromising the theoretical consistency of the

model. First, regional lumber supply equations were

estimated in inverse form so that regional lumber prices can

be obtained directly. Second, the regional factor market

relationships were reduced to single equations with price as

the dependent variable. The linkages between the product and

stumpage sectors in each region was thus established by

directly relating prices in the two markets. Third, in the

demand equations for regional lumber outputs, quantities

were replaced by identities that represented actual market

shares. Finally, in the market share equations, a regional

"accessibility index" was included to represent regional

locational advantage. These modifications helped simplify

the model structure considerably. The resulting system, its

components and interactions are illustrated in Figure 9.

The complete system to be estimated may be represented

as:

56

Endogenous Exogenous Aggregate product market: bllQ b12P allxl ( 1)

Regional stumpage market: b24Pp b25Ps a21x2 (2)

Regional product market: b3lQ b32P b33S b34Pp b35Ps a3lx3 (3)

where,

Q and P are, each 2x35 vectors of, respectively, aggregate

quantities consumed and average prices for both lumber and

plywood;

Pp is a 6x35 vector of regional mill level prices of lumber

and plywood;

Ps is a 4x35 vector of regional stumpage prices;

S is a 7x35 vector of supply region lumber and plywood

quantities;

Xl' X2 and X3 are vectors of predetermined variables; and

bll , b12 , b2l , b22 , b3l , b32 , b33 , b34 , b35 , all' a2l , and

a3l are arrays of coefficient estimates for endogenous and

predetermined variables with their appropriate dimensions.

There are four equations in (1), one aggregate demand

and one aggregate supply relationship for each of the two

products. (2) contains four equations, they are regional

stumpage price relationships. There are thirteen equations

in (3); four regional lumber price relationships; four

relationships representing supply of, and demand for, ply­

wood in the N. W. and the South; and five regional lumber

market share equations, including Canadian imports.

57

Exogenous ... Aggr. Prod . Variables P" Demand

Import _ ... Product Prices r- Imports ....

~,

Aggr. Prod. ...... ... Aggr. Prod • Supply """ ~ Price

~

product~vi~ Reg~onal ......

Rates ~ Prod. Supply

Wage ..

I Inventory ~---. , Regional .... _ .. Regional

stump. Price .... r- Prod. Price Inst~tution-~ al Factors

~ ..-Regional

~ Relative

Exports Reg. Prices

Transport .. Regional Costs r Mkt. Shares .. ..

Figure 9. Model structure and its main interactions.

Following a general explanation of the estimation

procedures and presentation of results, we will describe

each of these model components separately and in detail;

and will provide theoretical justifications for the forms

used in the final estimating structures.

58

MODEL ESTIMATION

As a first approximation, all parameters of the

behavioral equations in the model were estimated via

Ordinary Least Square (OLS). This was done to ascertain the

appropriateness of specifications; and to test the goodness

of fit in individual relationships. In several cases this

procedure led to some modification in the equations under

study.

The model contains several interdependent relation­

ships. Two Stage Least Square procedure was therefore used

as the estimation method for all relationships where one or

more of the explanatory variables were endogenously deter­

mined. Since the model contains a large number of exogenous

variables, in order to avoid problems with degrees of

freedom, it was necessary to select only a subset of

predetermined variables as instruments in the first stage.

Traditionally, the problem of choice among predeter­

mined variables has been dealt with either through arbitrary

selection of a small set of regressors, or by using a

principal components method to derive linear combinations of

predetermined variables that maximizes their covariance (for

the original presentation of the latter approach see Kloek

and Mennes, 1960). The first procedure is obviously faulty

and can lead to serious errors in specification. The second

procedure, though it has been shown to produce efficient

59

estimates in large samples, can cause confusion in the

theoretical interpretation of the mixture of variables.

In order to maintain procedural consistency in

selection of first stage regressors, a method was adopted

based on guidelines suggested by Fisher (1965) and McCarthy

(1971). The procedure was as follows: for each explanatory

endogenous variable, a set of regres30rs was selected that

include: 1) all predetermined variables in the equation

containing the endogenous variable, 2) all exogenous

variables in the equation that explains that variable, and

3) any lagged values of the endogenous variable present in

the model. Additional first stage regressors were then drawn

from other parts of the model by causal ordering of

variables in the entire system and choosing only variables

of the first causal order, i.e., variables that were judged

to be directly related to the equation under study.

An additional complication in the estimation of the

model arises from the contemporaneous correlation between

the disturbance terms in the lumber market share equations.

This problem emerges from the implied restriction that the

market shares must sum to unity, or 100 percent, so that in

any given period an over (under) estimation of one region's

market share is bound to lead to under (over) estimation of

other regions' market shares. To deal with this problem, the

lumber market share equations were estimated as a separate

block by the more appropriate method of Three stage Least

60

Square (Zellner, 1962; Zellner and Theil, 1962).2 The

decomposition of the model in this fashion is justified

because no current endogenous variables appear on the

right-hand side of these equations. Verification by the

order condition shows that the identification requirement of

the Zellner procedure is also satisfied. In the NW market

share equation this procedure resulted in an unreasonably

small coefficient on the accessibility index. These

equations were subsequently reestimated with imposed

restriction that the coefficient on the accessibility index

(see Table XIV) for NW should equal the value obtained from

the OLS estimate. The estimation results of the complete

model are presented in Table VIII. For the definitions of

variables, their derivation and sources see Table IX.

TABLE VIII

PARAMETER ESTIMATES OF THE MODEL

(1) Lumber Demand (Aggregate Consumption) TLUMCON = 34867.25 - 64.07*LUMPRUS - 31050*MAL/PLY +

(2.5) (4.1) 9.19*PISSPRD + 10.28*MAHSTRT + 21.20*PERSINC (1.6) (6.5) (2.7)

DW = 1.64 Estimation Method: 2SLS 2 R = .842

(2) Lumber Consumption Identity TLUMCON = TLUMPRD + TLUMIMP - TLUMEXP

2 The method is based on simUltaneous solution of all parameters of the system using the variance-covariance of the disturbance terms of equations. For a complete description of the method see Johnston (1984, pp. 486-90) and Pindyck and Rubinfeld (1981, pp. 334-6).

61

(3) Average Price of Lumber in u.s. LUMPRUS = -37.16 + 0.238*LUMPRUS_1 + 0.000994*TLUMCON +

(1.93) (1.72) 1.665*STMPRUS + 19.77*RW/ILPL (3.3) (4.0)

R2 = .844 DW = 1.30 Estimation Method: 2SLS

(4) Plywood Demand (Aggregate consumption) TPLYCON = - 7356.4 - 8.30*PISWPLY - 183.1*MAPLY/S +

(1.1) (0.2) 154.68*VNCONST + 72.57*INDINDP (3.5) (1.8)

R2 = .967 DW = 1.56 Estimation Method: I2SLS

(5) Plywood Supply TPLYPRD = 7105.7 + 4.14*PISWPLY - 2656.0*RW/ILPP +

(1.05) (2.4) 0.699*TPLYCON

R2 = .955 DW = 1.51 -lstimation Method: 2SLS

(6) Stumpage price NW STMPRNW = 47.20 + 0.005*TTCUTNW_1 + 0.413*LUMPRNW -

(1.23) (6.0) 0.0015*INVPRNW - 0.0047*TVSNFNW (4.7) (0.61)

R2 = .861 DW = 1.38 Estimation Method: 2SLS

(7) stumpage Price so STMPRSO = 0.954 + 0.988*STMPRSO_1 + 0.654*LPCHGSO

(11.1) (6.5) R2 = .803 DW = 1.88 Estimation Method: 2SLS

(8) stumpage Price SW STftPRSW = -11.72 + 0.0092*TTCUTSW_1 + 0.485*LUMPRSW -

(2.0) (13.8) 0.00087*INVPRSW - 0.021*TVSNFSW (2.5) (2.3)

R2 = .955 DW = 2.2 Estimation Method: 2SLS

(9) stumpage Price IL STMPRIL = 1.86 + 0.853*STMPRIL_1 + 0.235*LPCHGIL

(13.3) (7.1) R2 = .873 DW = 2.31 Estimation Method: 2SLS

(10) Price of Lumber NW Region LOMPRNW = -33.9 + 0.26*LUMPRNW_1 + 0.0056*LUMPDNW +

(2.0) (4.9) 0.917*STMPRNW + 4.09*LCSTLNW

(5.6) (1.7) R2 = .829 DW = 1.63 Estimation Method: 2SLS

62

(11) Price of Lumber SO Region LUMPRSO = -19.9 + 0.339*LUMPRSO_l + .0046*LUMPOSO +

(2.9) (3.5) 0.73*STMPRSO + 0.72*IRLWRSO - 0.26*ILPOLSO

(0.6) (4.4) (3.8) R2 = .760 OW = 1.65 Estimation Method: 2SLS

(12) Price of Lumber SW Region LUMPRSW = 26.51 + O.23*LUMPRSW_

l + 0.0039*LUMPOSW +

(3.2) (1.65) 1.34*STMPRSW + 0.03*IRLWRSW

(7.6) (1.23) R2 = .960 OW = 1.98 Estimation Method: 2SLS

(13) Price of Lumber IL Region LUMPRIL = 1.55 + 0.286*LUMPRIL_

l + 0.0029*LUMPOIL +

(2.4) (.62) 1.29*STMPRIL + 12.8*LCSTLIL

(2.4) (2.7) R2 = .805 OW = 1.83 Estimation Method: 2SLS

(14) Plywood Supply NW PLYPDNW = 2173.1 + 0.962*PLYPONW_ l + 13.3*PLYPIOF -

(10.1) (1.0) 33.13*STMPRNW - 834.7*LCSTPNW (1.5) (1.3)

R2 = .904 DW = 1.74 Estimation Method: 2SLS

(15) Plywood Supply SO PLYPDSO = -1999.7 + 0.742*PLYPOSO_ l + 18.05*PLYPISP +

(9.3) (2.5) 4.87*ILPOPSO

(1. 42) R2 = .981 DW = 2.16 Sample 1965-84, OLS

(16) Market Share Lumber Canada MKTSLCA = 9.237 + 0.938*MKTSLCA_l - 8.886*MACA/US

(14.4) (1.4) R2 = .967 OW = 1.30 Estimation Method: OLS

(17) MKTSLCA = 100 * (LUMIMPC / TLUMCON)

(18) Market Share Lumber NW MKTSLNW = 1.27 + 0.934*MKTSLNW_l + 0.218*(LPUS-NW) +

(12.4) (2.3) 0.095*ACCSLNW

2 (--) R = .914 OW = 2.1 Estimation Method: 3SLS

(19) MKTSLNW = 100 * [(LUMPONW - EXPLUNW) / TLUMCON]

(20) Market Share Lumber SO MKTSLSO = 9.29 + 0.0017*LUMPDSO_1 + 0.152*(LPUS-SO) +

(7.0) (1.9) 0.0082*ACCSLSO

2 (1.4) R = .610 DW = 1.36 Estimation Method: 3SLS

(21) MKTSLSO = 100 * [(LUMPDSO - EXPLUSO) / TLUMCON]

(22) Market Share Lumber SW

63

MKTSLSW = 7.82 + 0.00147*LUMPDSW_1 + 0.149* (LPUS-SW) + (7.1) (9.0)

0.00876*ACCSLSW 2 (2.0)

R = .923 DW = 1.58 Estimation Method: 3SLS

(23) MKTSLSW = 100 * [(LUMPDSW - EXPLUSW) / TLUMCON]

(24) Market Share Lumber IL MKTSLIL = 1.69 + 0.815*MKTSLIL_1 + O.0667*(LPUS-IL) +

(9.6) (1.5) O.00065*ACCSLIL

2 (0.9) R = .738 DW = 2.42 Estimation Method: 3SLS

(25) MKTSLIL = 100 * [(LUMPDIL - EXPLUIL) / TLUMCON]

(26) Demand for NW Plywood PLYPDNW = 15369.1 + O.239*TPLYCON - 9658.1*MANW/SO +

(5.5) (11.9) 149. 62*ACCSPNW

2 (3.4) R = .926 DW = 1.97 Sample 1965-84, 2SLS

(27) Demand for SO Plywood PLYPDSO = 5784.9 + 0.719*TPLYCON - 16289.8*MASO/NW +

(8.0) (7.4) 184.4*ACCSPSO

2 (1.4) R = .936 DW = 1.51 sample 1965-84, 2SLS

Figures in parantheses are t statistics.

TABLE IX

DESCRIPTION OF VARIABLES USED IN THE MODEL

ACCSLNW Accessibility index for NW lumber, defined in text.

ACCSLSO Accessibility index for SO lumber.

ACCSLSW Accessibility index for SW lumber.

ACCSLIL Accessibility index for IL lumber.

ACCSPNW Accessibility index for NW plywood.

ACCSPSO Accessibility index for SO plywood.

EXPLUNW Exports of lumber from NW (MMBF) [2, 3, 18].

EXPLUSO Exports of Southern Pine (MMBF) [3, 4, 18]

EXPLUSW Exports of lumber from California ports (MMBF) [2, 3].

EXPLUIL Exports of lumber from IL (MMBF) [2, 3, 4,].

64

I LPDLSO Index of labor productivity (MBF per man-year) in lumber production in SO (1967=100) [5, 6].

ILPDPSO Index of labor productivity (MFt. 2 per man-year) in plywood production in SO (1967=100) [5, 7].

INDINDP Index of industrial production (1967=100) [8].

IRLWRSO Index of hourly earnings in lumber and wood products industries SO (1967=100). See text for derivation [9].

IRLWRSW Index of hourly earnings in lumber and wood products industries SW (1967=100). See text for derivation [9].

INVPRNW Total private inventory of timber (forest industry and other privale holders) at the start of the period NW. (MMFt. ) [1].

INVPRSW Total private invento3y of timber at the start of the period SW. (MMFt. ) [1].

LCSTLNW Labor costs in lumber production NW. Derived by dividing real wage rates by the index of labor productivity in NW sawmills [9, 5, 6].

LCSTLIL Labor costs in lumber production NW. Derived by dividing real wage rates by the index of labor productivity in IL sawmills [9, 5, 6].

65

LCSTPNW Labor costs in lumber production NW. Derived by dividing real wage rates by the index of labor productivity in NW plywood mills [9, 5, 6].

LPUS-NW (LUMPRUS-LUMPRNW).

LPUS-SO (LUMPRUS-LUMPRSO).

LPUS-SW (LUMPRUS-LUMPRSW).

LPUS-IL (LUMPRUS-LUMPRIL).

LPCHGSO (LUMPRSOt - LUMPRSOt _1)·

LPCHGIL (LUMPRILt - LUMPRILt _1) •

LUMIMPC Lumber imports from Canada (MMBF) [1] •

LUMPDNW Lumber production in the NW (MMBF) [1] •

LUMPDSO Lumber production in the SO (MMBF) [1] •

LUMPDSW Lumber production in the SW (MMBF) [1] •

LUMPDIL . Lumber production in the IL (MMBF) [1] . . LUMPRNW Price of softwood lumber NW, f.o.b. mill, $/MBF

(Deflated by All Commodity PPI) [1].

Ltn{PRSO Price of softwood lumber SO, f.o.b. mill, $/MBF (Deflated by All Commodity PPI) [1].

LUMPRSW Price of softwood lumber SW, f.o.b. mill, $/MBF (Deflated by All Commodity PPI) [1].

LUMPRIL Price of softwood lumber IL, f.o.b. mill, $/MBF (Deflated by All Commodity PPI) [1].

LUMPRUS Weighted average f.o.b. mill price of all producing regions including Canadian imports, deflated by All Comma PPI.

MACA/US Two-year moving average ratio of price of Canadian lumber to average price of lumber in U.S., both prices in U.S. currency [1, 10].

MAHSTRT Two-year moving average of housing starts in U.S. [11, 12].

MAL/PLY Two-year moving average ratio of Producer Price Index for softwood lumber to the Producer Price Index for softwood plywood.

66

MAPLY/S Two-year moving average ratio of PPI for softwood plywood to composite index of sUbstitutes: PISWPLY /(.S*PPI particle boards + .2S*PPI gypsum products + .2S*PPI building paper and board) [13, 14].

MANW/SO Two-year moving average of (PLYPIDF / PLYPISP).

MASO/NW Two-year moving average of (PLYPISP / PLYPIDF).

MKTSLCA Canadian lumber imports as percent of total u.s. consumption. [1]

PERSINC Aggregate national personal income (MMM$), deflated by GNP Implicit Price Deflator (1972=100) [15].

PISWPLY Producer price index for all softwood plywood (1967=100) [13, 14].

PISSPRD Producer price index for structural steel products (1967=100) [14].

PLYPDNW Plywood production in the NW (MMBFt.2) [1].

PLYPDSO Plywood production in the so (MMBFt.2) [1].

PLYPIDF Price of Douglas fir plywood, deflated by All Comm. PPI. (Index 1967=100) [1].

PLYPISP Price of Southern pine plywood, deflated by All Comm. PPI. (Index 1967=100) [1].

RW/ILPL Real hourly earnings in lumber and wood products industry in u.s. divided by the index of output per employee in sawmills [9, 16].

RW/ILPP Real hourly earnings in lumber and wood products industry in u.s. divided by the index of output per employee in plywood mills [9, 16].

STMPRNW Average price of timber harvested from National Forests in the NW, $/MBF, (deflated) [1].

STMPRSO Average price of timber harvested from National Forests in the SO, $/MBF, (deflated) [1].

STMPRSW Average price of timber harvested from National Forests in the SW, $/MBF, (deflated) [1].

STMPRIL Average price of timber harvested from National Forests in the IL; $/MBF; (deflated) [1].

STMPRUS Weighted average price of timber harvested from National Forests in all regions, 1967 $/MMBF.

TLUMCON Total apparent domestic consumption of softwood lumber, MMBF [1].

67

TLUMEXP Total annual exports of softwood lumber, MMBF [1].

TLUMIMP Domestic imports of softwood lumber from all origins, MMBF [1].

TLUMPRD Total domestic lumber production, MMBF [1].

TPLYCON Total apparent2domestic consumption of softwood plywood, MMFt. •

TTCUTNW Total annual3harvest of timber by all ownerships in NW, MMFt. •

TTCUTSW Total annual3harvest of timber by all ownerships in SW, MMFt. [ 1] •

TVSNFNW Total annual volume of timber3auctioned from National Forests in NW, MMFt. [I, 19].

TVSNFSW Total annual v9lume of timber3auctioned ~rom National Forests in SW, MMFt. [I, 19].

VNCONST Total value of new construction put in place, deflated by the GNP Implicit Price Deflator (1972=100) [17].

* Numbers in brackets indicate sources of data as listed in Appendix A.

3 All volumes of timber auctioned and sold from National Forests were converted from BF, local log rules to cubic feet. The appropriate conversion factors were provided by Dr. R.W. Haynes at the PNW Forest and Range Experiment station in Portland, Oregon. These conversion factors are: Western Oregon and Washington: 5.5~ Eastern Oregon 2nd Washington: 4.96; SO: 4.67; SW: 5.27; IL: 4.67 BF per Ft ••

68

MODEL COMPONENTS

The Aggregate Product Market

The four equations in this part of the model represent

a simple supply-demand relationship for each of the two

products. The postulated relationships in these equations

are essentially the same as the conceived structures set

forth in Chapter I. Their specifications are common to

several other econometric studies of the wood products

industry, as well as other commodity models.

In the demand equations, quantities of aggregate

product demand (apparent consumption) are related to own

price, price of sUbstitutes and one or more measures of the

level of activity in relevant end-use markets. The choice of

the latter variables, sometimes referred to as "shifters"

(since they serve to locate the function), is based on our

discussion of end use markets in Chapter II.

Another component of the demand relations is the

substitution effect. The problem of correctly identifying

patterns of SUbstitution among commodities is a serious one

and merits careful consideration. Forces of technological

change are, more often than not, quite unpredictable. New

products appear on the market on short notices; and old ones

disappear from the face of the market unnoticed. Indeed, as

Pringle (1971) has pointed out, many cases of substitution

in the forest products market have been the result of

development of new and often superior products, especially

within the industry itself. In such cases, reliance on the

69

conventional price considerations to explain substitution,

may be inappropriate. Due to the time related nature of

these developments, the time dimension in demand analysis,

therefore, becomes crucial. The longer the period of

analysis, the higher the likelihood of error.

In our analysis, plywood and structural steel prices

are included in the lumber demand relation to account for

the SUbstitution effect. In case of plywood, the moving

average ratio of plywood price index to a composite index of

three substitutes is used (see Table IX). In both cases the

commodities considered are established products with a long

history of competition with the product under study.

The aggregate product supply functions are also

conventional in form, except that the lumber supply equation

is expressed in terms of price. The average price of lumber

in the national market is determined by its own value in the

previous period, total quantity consumed, average price of

stumpage from all regions, and real wage rates (hourly

earnings) in the industry. In order to account for the

offsetting influence of historical gains in productivity on

the rising cost of labor, wage rates in both relations are

adjusted by the BLS indexes of labor productivity for saw­

mills and planing mills (SIC 2421) and plywood (SIC 2430) •

Regional stumpage Markets

Direct estimation of structural relationships in the

regional stumpage markets posed many serious problems.

70

Differential patterns of ownership among regions, diversity

of economic objectives pursued by the private holders within

each region, and combination of various species in each

geographical area are but a few of the factors contributing

to the complexity of this market. It is therefore not

surprising that the majority of previous empirical studies

of the timber economy have resorted to somewhat ad hoc

specifications in explaining the behavior of this market.

The approach adopted here begins with the stipulation

that the derived demand behavior for stumpage is more

appropriately described in a dynamic setting. Firms

producing the final products, i.e. lumber and plywood,

usually do not plan their levels of output in the spur of

the moment. Adjustments in capacity and input flows, and

employment decisions, produce rigidities in their supply

adjustments that require some advance planning (Adams 1977,

p. 20). In addition, due to the relatively low short-run

price elasticities of demand for lumber and plywood, much of

the increase in factor price (i.e. stumpage) can be

transmitted to the final product market. It is therefore

unlikely that producers' demand for stumpage would adjust

immediately to changed conditions of price.

We can therefore postulate that the "expected" level

of demand for stumpage is given by:

(3.1)

71

where Pt and Plt are, respectively, current stumpage and

lumber prices. However, due to the constraints discussed

above, we would expect the actual demand to adjust only

partially to the expected level, that is:

(3.2)

which, by substitution and rearrangement of coefficients to

estimable forms, gives the following estimating relationship

that is indeed the partial adjustment model widely appli9d

to agricultural commodities (Nerlove, 1958a, 1958b):

(3.3)

On the supply side, we assume that harvest levels are

determined by stumpage prices and other supply determinants.

In our analysis we relate stumpage supply directly to price,

and inventory levels at the start of the period (INV). Also,

we include timber offerings from the National Forests (QNF)

as an additional shift variable so that the stumpage supply

relationship is expressed as:

(3.4)

Equations (3.3) and (3.4), together with the implied

equilibrium condition, provide all the information we need

on the regional stumpage markets. Given these simultaneous

72

relationships for each region, it is possible to obtain an

estimating relationships for stumpage price directly from

the reduced form of equations (3.3) and (3.4) by regressing

Pt on all the exogenous variables in the system.

In estimation, the above formulation produced

satisfactory results only for the NW and SW markets. In the

case of the Southern stumpage, the coefficient for the

National Forest offerings, contrary to our expectation,

carried a positive sign. In the Inland region, on the other

hand, although the coefficients all had the right signs, two

were found to be statistically insignificant. An even more

serious problem in the case of the Inland region proved to

be the presence of very high serial correlation and the fact

that corrective procedures led to incorrect signs on two

coefficients. These results are reported below. Note that

the inventory volume for the Inland region has been replaced

by the ratio of total private harvest to private inventory.

(3.5) STMPRSO = -37.09 + 0.482*LUMPRSO + 0.0685*TVSNFSO + (5.9) (7.5) (1. 8)

0.0064*TTCUTSO_1 - 0.0957*INVPRSO (3.6) (0.7)

2 _ R - 0.871 OW = 1.69

(3.6) STMPRIL = -6.39 + 0.296*LUMPRIL - 0.0008*TVSNFIL + (29) (6.6) (0.19) 0.02l*TTCUTIL_1 + 0.224*CUT/IIL (2.7) (0.08)

R2 = 0.777 OW = 0.944

73

Due to these difficulties an alternative approach is

adopted. It is based on a simplified derived demand approach

and is a variant of the price mark-up procedure applied to

the analysis of many agricultural commodity prices (Tomek

and Robinson 1952) and the stumpage price projections in the

USDA 1982 analysis of the timber situation in the United

states (USDA/FS 1982, pp. 150 and 212).

In its most simplified and general form, the method

invo1 ves the establishment of a relationship between the

product market and the factor market in terms of a marketing

margin:

(3.7) PP = FP + MM

or inversely,

(3.8) FP = PP - MM

where PP is the product price, FP is the factor price, and

MM denotes the marketing margin.

Haynes (1977) has suggested several possible forms for

the linkage between the two markets based on alternative

treatments of the marketing margin as either constant, a

constant percentage, or a linear function of prices. In the

case of the latter, stumpage prices are regressed on product

prices and the coefficient on the product price is

74

interpreted as the coefficient or elasticity of price

transmission between the two markets according to whether

the prices are expressed in logarithms or not. In our study

the relationship between stumpage price and lumber price

follows a specification that has come to be known as the

"pass-through" technique in the forestry literature (Haynes

ibid., p.284). It involves an expression relating the price

change in the two markets. The implication here is that

changes in the product market are only partially transmitted

to the stumpage market; i.e.

(3.9)

This relationship was used to estimate stumpage prices in

all four regions. As indicated by the statistical properties

of the estimates shown in Table X, the relationship appears

to adequately depict the linkages between regional stumpage

and product prices in all regions. Note that the

coefficients on lumber price change measure the extent to

which changes in product prices are transmitted to the

stumpage market, and thus reflect the elasticity of supply

in regional stumpage markets. The results in Table X

indicate that for a shift in demand for regional lumber,

greater stumpage price changes in the SO than in the NW

would be expected. The elasticity of regional stumpage

supplies has been examined in several other studies such as

Adams (1976), Haynes (1977), and Adams and Haynes (1980). A

75

comparison of findings from these studies indicate that the

stumpage market in the SO has lost much of its fluidity over

the past two decades. In the light of relatively significant

declines in NW stumpage prices during the past ten years, it

is not surprising to find a higher elasticity in the NW

stumpage market than in the so.

The results of this latter formulation were used to

represent the product-stumpage linkage in the South and

Inland regions. No attempts were made to incorporate the

inventory and National Forest offerings in this formulation.

TABLE X

ESTIMATION RESULTS FOR REGIONAL STUMPAGE PRICE RELATIONSHIPS

STMPRNW = 2.55 + 0.932*STMPRNW_1 +

2 (15.6) R = 0.889 OW = 1.96

STMPRSO = 0.95 + 0.988*STMPRSO_ l +

2 (ll.l) R = 0.803 OW = 1.88

STMPRSW = 2.30 + 0.909*STMPRSW_1 +

2 (17.3) R = 0.920 OW = 2.3

STMPRIL = 1.86 + 0.853*STMPRIL_ l +

2 (13.3) R = 0.873 OW = 2.04

0.281(LUMPRNW - LUMPRNW_l

) (4.6)

0.654(LUMPRSO - LUMPRSO_l

) (6.5)

0.454(LUMPRSW - LUMPRSW_l

) (9.8)

0.235(LUMPRIL - LUMPRIL_l

) (7.1)

The reason is that although both variables are important

indicators of supply behavior in the long-run, they are

unlikely to resu1 t in the loss of much information in a

76

short-run analysis. Their omission, however, does somewhat

limit the utility of the model in the area of policy

analysis. This is, nevertheless, a small loss within the

context of the model as a whole.

A complete analysis of the regional stumpage markets

requires a different and more appropriate setting than the

present one. The impact of the Forest Service policies

regarding harvest levels, for instance, can more amply be

analyzed within the framework of regional private stumpage

markets. For, as Haynes and others (1981), and Connaughton

and Haynes (1983) have shown, the relative impact of changes

in the National Forest offerings on local stumpage prices

depend largely on the behavior of private owners; and their

reaction --or ability to react-- to the changing price

conditions. In other words, if the stumpage supply from

private ownerships is elastic, then we can expect the effect

of changes in National Forest offerings to be mitigated by

adjustments in the private supply.

In order to examine this proposition, price

elasticities of private stumpage supply were estimated for

the four regions. The analysis is based on a simple

regression equation that relates supply of stumpage from all

private ownerships ("forest industry" and "other private"

owners) in a given region to the price of stumpage and

inventory levels in that region. The results are tabulated

in Table XI. The aim of the analysis is purely illustrative.

It is intended to measure possible losses of information

77

incurred as a result of omissions in our approach to

modeling the stumpage price in the SO and IL regions. Though

the statistical properties of these estimates were in

general satisfactory, the resulting low coefficients of

determination (between .57 to .79) and serial correlation in

some cases, precluded the use of these relationships in our

model.

The observed variations in cross regional supply

behavior in the private stumpage markets, as indicated by

these elasticity measures, is considerable. stumpage price

elasticities in the NW and so are shown to be higher than

those found in other regions. Inventory, on the other hand,

appears to be a much more important factor in determining

supply patterns in the SW and IL regions. These results are

generally consistent wi th those found by previous studies

for example Adams (1977), Adams and Haynes (1980), and

Adams, et.al. (1982). One important implication of these

TABLE XI

ESTIMATES OF REGIONAL ELASTICITIES OF PRIVATE STUMPAGE SUPPLY

. . . * Elast~c~t~es

supply Region Stump. Price Inventory

NW 0.493 0.732 SO 0.458 0.162 SW 0.135 1.564 IL 0.111 1.073

* Point estimates measured at means for each variable.

78

results is that the impact of public timber offerings will

probably be much smaller in the SO and NW than in the sw and

IL regions. with regards to the inventory levels, on the

other hand, it seems that resource availability is a much

more constraining factor for the suppliers in SW and IL than

in NW, and especially the SO region. Empirical evidence of

rapid expansion of private inventories in the South during

the sample period also support this conclusion.

Regional Product Markets

This part of the model contains a total of thirteen

equations: four relationships for regional lumber prices,

four relationships for plywood supply and demand in NW and

SO, and five regional market share relationships. The

regional lumber price and plywood supply relations are

specified in forms identical to the aggregate market

relations. All equations include labor productivity,

expressed in terms of physical output per man-year in each

period. It is calculated by dividing annual regional output

by the average number of production workers. Inadequate

regional or state level data precluded the construction of

more suitable measures such as value added per employee. The

productivity measure is employed here as a surrogate for

technological change in the industry over time. See Appendix

C for data.

Technological change is defined here in the positive

sense of the development or adoption of more efficient

79

production techniques such that greater output can be

obtained from a given combination of inputs. But this

conclusion (technological change) cannot be inferred

directly from the data. An alternative --and equally valid--

explanation of the movements in this measure is economies of

scale. In other words, the over time variations in the

output/employment ratio may be interpreted as actual shifts

in the production function, or movements along the same

function. If the latter is indeed the case, then we can

expect the productivity measure to be highly correlated with

output and lead to collinearity problems in estimation of

supply functions.

We have therefore used this measure with caution. In

all cases where the index of productivity exhibited a high

correlation with output, it was either excluded from the

relationship, or used as a deflating factor to adjust real

wage rates.

Regional wage rates in the lumber and wood products

industry (SIC 24) were calculated as the average of hourly

earnings in the industry in the major producing states in

that region. 4 This data, however was not available for the

entire sample period. Industry-specific data on hourly

4 The regional averages are based on data from a select number of leading states. They are; NW: Oregon and Washington; so: Texas, S.Carolina, Florida, Georgia, Luisiana; SW: California; IL: Idaho, Colorado, Montana, Utah, and N.Mexico.

80

earnings at the state level are generally available only

from 1972 as reported by the Bureau of Labor statistics. The

remainder of the series from 1950 were estimated by first

constructing an index of average regional hourly earnings in

manufacturing (with 1967 as the base) from the state level

data; and then applying this index to the first available

observation in the series to calculate the rest of the

observations. These data are reported in Appendixe B.

In order to check the accuracy of these estimates, a

second procedure was adopted for deriving the same

estimates. This latter procedure consisted of adjusting

weighted regional average hourly earnings in manufacturing

by the weighted ratios of hourly earnings in manufacturing

to average hourly earnings in the lumber and wood products

industry at the national level in each period; i.e., for

each region,

(3.9) EMPLWPt*AVWRLWPt EMPLWPUSt*AVWRLWPUSt = EMPMFGt*AVWRMFGt EMPMFGUSt*AVWRMFGUSt

where the first two terms are respectively regional wage

rates in lumber and wood products, and manufacturing; and

the terms on the right-hand side are the same variables at

the national level. The results from both procedures were

quite close and produced identical results in estimation.

The two regional plywood supply equations were

specified according to the classical partial adjustment

81

model and include a one-period lagged quantity term, own

price, and factor prices as explanatory variables.

Estimation of the plywood equation for the Southern

plywood produced a positive sign on the stumpage price vari­

able. The stumpage price term was consequently dropped in

final estimation. This result, though contradictory to the

postulated relationship, may have an explanation. Softwood

plywood is a relatively new product in the Southern market

and has expanded very rapidly during the past decade. Expan­

sion of plywood output has in turn intensified local com­

petition for stumpage, leading to higher prices in the

stumpage market. Hence, the positive correlation is

justified; yet the stumpage price term cannot be retained

because the causal inference with respect to the direction

of causation, as implied by the supply equation, is no

longer valid.

Regional Market Shares

The seven equations in this part of the model

constitute the pivotal relationships in our model and

comprise the very core of the analysis. structurally, all

other components of the model can be viewed as peripheral to

this set in the sense that the information they provided is

ultimately channeled into this set of relationships.

These equations are all essentially similar in form

and structure; except that the two plywood share equations

are expressed in terms of total regional output. Regional

82

market shares in plywood are therefore obtained indirectly

from the ratio of output estimates to total consumption at

the national level. In estimation, regional exports of

plywood were ignored because they constitute a small

percentage of regional production and the volumes are very

close in both regions. The plywood market share equations

were estimated for both regions over the sample period

1965-1984. The reason is that the advent of plywood

production in the South represents a major transformation in

the competitive structure of the plywood market. Since

practically no plywood was produced in the South before

1964, the behavior and position of the NW prior to this date

would be of little relevance to the analysis of competition

in this market.

Each equation contains a measure of price competitive­

ness which is expressed either in terms of price ratios (in

plywood equations), or price difference (in lumber

equations). In the market share equation for Canadian

imports, the price of Canadian lumber is measured in u.s.

dollars. Thus the impact of fluctuations in currency

exchange rates are incorporated in the price term. All

market share relationships for lumber contain a lagged

output term. The underlying justification for this

formulation is that changes in interregional trade patterns

do not respond instantaneously to small changes in market

conditions. In view of the relatively low elasticities in

regional supply and demand conditions that prevail in the

83

lumber and plywood markets, this is indeed a very reasonable

assumption. In the lumber market share equations for the NW

and IL regions the lagged output terms were replaced by the

regional market shares in the previus period. Since in both

regions, the NW in particular, exports constitute a

sUbstantial share of the total output, the use of the lagged

output term appeared inappropriate in that they lead to over

estimation of actual shares of the domestic market.

The other major component of the market share

equations is the regional accessibility index which

represents relative locational advantage of each region.

These measures are intended to approximate the overall

economic accessibility, or, the potential of each region in

marketing its outputs. Construction of this index is based

on the principle of "potential interaction" as employed in

the context of general gravity models.

Gravity models constitute a large family of flexible

methods widely applied to a range of analytic situations

involving interaction between spatially separated nodes. The

general approach in gravity models is predicated on the

physical law of mass gravitation. It explains gravitation

(or interaction) between two points in space in terms of

some surrogate measure of their respective masses, and as a

decreasing function of the distance between them. Among the

many different forms of the gravity model used in trans­

portation and migration analysis, the types that are of

84

relevance to the present study are the commodity flow 5 variants. As distinct from the more general forms of the

gravity models that measure interaction "between" two

points, commodity flow models are based on the "potential"

concept of gravity that pertains to the measurement of

potential interaction at a given area or point. Within the

context of commodity flow analysis, the most general

formulation of the potential gravity model may be given as:

(3.10) F .. = bO. f(d .. ) 1) ) 1)

where Fij is the commodity flow from i to j, OJ is a measure

of demand at j for the commodity under question, d.. is 1)

distance or a measure of transport cost between the two

points, and b is a constant. 6

Our presentation of regional accessibility is based on

a formulation of the gravity model given by Isard (1960 p.

499). It is defined as:

5 Attempts at formalization and theoretical derivation of the gravity model have followed two distinct paths: the probabilistic approach of Isard (1960, pp. 493-502) and Wilson (1967); and the economic approach based on the utility theory set forth by Niedercorn and Bechdolt (1969). For a comprehensive treatment of the gravity model see Isard, ibid. pp. 493-566.

6 This formulation and parts of the discussion are borrowed from Richardson (1979 pp. 194-5).

85

(3.11)

where Ai is accessibility of the supply region i, Dj denotes

level of demand in region j, and TC.. is the average ~J

transport cost between i and j for all demand regions. Two

different indexes of accessibility were constructed using

ei ther personal income or annual change in population to

approximate levels of regional demand for lumber and ply­

wood. Both variables are highly correlated with the level of

construction activity and are potentially appropriate

surrogates for wood consumption. The second index, measured

in terms of population change, however, produced

consistently better statistical results in all equations and

was adopted. In regional market share equations for lumber,

the exponent to be applied to transportation costs was set

to equal one. An alternative formulation of (3.11) above,

wi th an exponent of two on transport costs ( a=2) produced

much better results in the plywood demand equations and was

consequently used. The obtained index numbers are shown in

Table XIV.

Interregional transport costs were derived for every

period in the sample by applying the Producer Price Index

for Wood Products Freight to the average 1977 estimates of

transport costs for lumber and plywood provided by the

Pacific Northwest Forest and Range Experiment station. See

Tables XII and XIII.

86

since the Bureau of Labor statistics began reporting

the Producer Price Index for Wood Products Freight in 1969

(see Fehd 1975), it was necessary to construct the remaining

series from 1950 indirectly. This was accomplished by

regressing the available observations on the Producer Price

Index for Transportation Services during the same sample

period. The missing observations were thus estimated from

the regression equation: PPIWPF = -32.571 + 1.265 [PPI

Trans. services] (R2=.99). See Appendix D.

From/To

NW

SO

SW

IL

From/To

NW

SO

SW

IL

TABLE XII

INTERREGIONAL TRANSPORT COSTS FOR LUMBER

1977 ($ PER MBFt., DEFLATED)

NW PSW IL NC NE

5.39 16.02 17.07 26.54 31.21

25.92 25.85 24.25 15.45 15.67

11.61 11. 72 17.68 26.78 31.24

21.25 19.38 8.61 24.18 28.95

TABLE XIII

INTERREGIONAL TR&~SPORT COSTS FOR PLYWOOD

1977 ($ PER MBFt. 2 , DEFLATED)

NW PSW IL NC NE

5.74 16.34 17.20 26.98 31. 72

29.22 29.22 26.60 15.65 16.69

11.81 11.91 17.97 27.23 31.69

22.15 20.25 8.75 24.58 29.43

87

SO

28.54

9.35

27.41

25.48

SO

27.82

9.50

27.79

25.90

88

TABLE XIV

REGIONAL INDEXES OF ACCESSIBILITY LUMBER AND PLYWOOD

Lumber Plywood

Year NW SO SW IL SO NW

1951 169.70 274.49 179.52 154.45 39.84 17.02 1952 169.38 244.31 182.08 162.50 26.82 14.51 1953 168.20 212.20 185.97 166.04 17.15 12.83 1954 183.39 255.95 190.81 177.65 22.88 14.28 1955 206.43 313.48 205.85 196.87 33.32 17.55 1956 205.99 296.47 213.85 196.04 31.82 17.70 1957 197.18 313.36 209.15 189.03 34.50 15.11 1958 178.10 271. 96 193.35 167.53 26.72 12.61 1959 177.48 269.11 188.39 168.56 26.32 12.92 1960 159.25 263.29 166.10 158.42 26.56 10.74 1961 166.65 256.03 182.14 166.73 23.86 10.59 1962 158.52 237.30 166.78 146.74 22.53 11.53 1963 146.83 223.35 160.30 139.73 19.97 9.34 1964 135.00 219.03 144.96 130.63 19.55 8.04 1965 122.43 193.07 129.19 115.42 16.78 7.66 1966 112.71 165.36 107.18 98.45 14.37 8.89 1967 105.17 143.56 100.84 89.89 11.95 8.47 1968 103.77 154.34 97.87 93.03 13.33 7.96 1969 108.92 148.87 106.01 94.54 12.23 8.34 1970 119.25 180.83 117.70 110.72 14.11 7.68 1971 129.88 223.84 132.83 128.79 18.05 6.90 1972 105.78 189.21 110.12 109.54 15.93 5.33 1973 107.42 177.65 110.51 104.94 16.92 6.92 1974 111.99 174.84 111.54 101.49 17.19 8.40 1975 115.18 175.80 115.18 105.03 16.43 8.41 1976 112.01 163.40 112.52 101.43 14.45 8.00 1977 121.08 167.91 119.84 108.20 14.49 8.95 1978 134.02 174.03 131. 25 116.25 14.85 10.52 1979 138.42 188.35 134.05 120.27 16.21 10.70 1980 139.73 193.04 136.83 119.65 15.23 10.36 1981 110.37 165.78 112.15 102.72 17.14 6.77 1982 70.32 140.53 71.01 74.62 17.20 3.18 1983 74.03 134.34 79.99 77.90 19.06 3.07 1984 69.13 131. 06 66.80 71.87 21.40 3.17

For derivation see text.

CHAPTER IV

MODEL VALIDATION

A model is, by definition, a representation of real

world phenomena. A "good" model, it hence follows, is one

that is true to the original. Likewise, the "goodness" of an

econometric model is evaluated by the extent of its accuracy

in depicting the economic system it intends to describe.

Evaluation of an econometric model, as Dhrymes and

others (1972) have pointed out, is a continuous process that

accompanies every step in model specification, estimation,

and implementation. There is a wide array of criteria,

parametric and otherwise, that can be used to evaluate

performance of econometric models. Choice of specific

criteria, and the degree of the stringency with which we

apply each, depend on the stage in model development and the

purpose for which the model is built. In this chapter we

will consider various properties of individual components of

the model developed in Chapter III and evaluate the perform­

ance of the model as a whole.

VALIDATION IN PARAMETER ESTIMATES

Construction of an econometric model involves much

more than the working out of a plausible configuration for

sets of seemingly related economic variables. The primary

90

Orcutt iterative procedure in the second stage of

estimation. In case of the latter equation, however, the

estimation method involved precluded the use of such

solution scheme and the original estimates were retained.

With the exception of two market share equations (the South

and the Inland regions), the statistical fit of all

equations, measured in terms of their respective

coefficients of determination, appear acceptable. Of the

total of seventy-two estimated coefficients in the model,

fifty-one are statistically significant at the .01 and

eleven more at the .1 level.

statistical significance of estimated coefficients is

a highly desirable property in an econometric model for it

shows the significance of the information conveyed by

particular data. Yet, statistical significance by itself

does not constitute sufficient ground for validity. The

estimated coefficients must also make sense. A second --and

perhaps a more relevent-- perspective on model validity can

be gained by examining the accuracy of model parameters.

There are, however, no formal procedures for insuring that

the coefficients are of the right magnitudes. The decision

as to what constitutes the right size for a given

coefficient is a judgemental one that depends on the

analyst's knowledge of the market under investigation.

Fortunately, the literature on the wood products

economy is rich with predictions about the magnitude of

certain effects. The more recent econometric studies, in

91

Orcutt iterative procedure in the second stage of

estimation. In case of the latter equation, however, the

estimation method involved precluded the use of such

solution scheme and the original estimates were retained.

with the exception of two market share equations (the South

and the Inland regions), the statistical fit of all

equations, measured in terms of their respective

coefficients of determination, appear acceptable. Of the

total of seventy-two estimated coefficients in the model,

fifty-one are statistically significant at the .01 and

eleven more at the .1 level.

statistical significance of estimated coefficient is a

highly desirable property in an econometric model for it

shows the significance of the information conveyed by

particular data. Yet, statistical significance by itself

does not constitute sufficient ground for validity. The

estimated coefficients must also make sense. A second --and

perhaps a more relevent-- perspective on model validity can

be gained by examining the accuracy of model parameters.

There are, however, no formal procedures for insuring that

the coefficient are of the right magnitudes. The decision as

to what constitutes the right size for a given coefficient

is a judgemental one that depends on the analyst's knowledge

of the market under investigation.

Fortunately, the literature on the wood products

economy is rich wi th predictions about the magni tude of

certain effects. The more recent econometric studies, in

92

particular, provide much insight in this area. An

examination of certain key parameters in the model such as

relative impacts of various exogenous variables and price

elasticities reveals that these estimates are quite compar­

able with those obtained in other studies.

The multiregional structure of the present model

imposes a further condition for evaluating the accuracy of

estimated coefficients: that for any particular behavioral

relationship, variations in functional properties across

various regions must be justifiable and reasonably consis­

tent with actual market experience in each region. This

condition was employed most intensively in construction of

regional market share relationships, where essentially

identical specifications are used across all regions. This

condition formed the basis for choosing among alternative

formulations of the accessibility index and price terms in

these equations.

cross-regional differences in response to movements in

various exogenous variables can be analyzed by examining the

relevant impact multipliers. Impact multipliers for regional

lumber outputs associated with selected explanatory

variables are reported in Table XV.

These multipliers are computed numerically by

successive sUbstitution of relevant equations in the model.

Multipliers associated with other exogenous variables not

reported in Table XV, can also be obtained in the same

fashion. Due to the rather complex structure of the access-

93

ibi1ity index, however, a simple analytical solution for the

impact multipliers associated with the Producer Price Index

for Lumber and Wood Products Freight is difficult to obtain.

The reported multipliers in this case were computed

numerically at the means for each variable. Figures in each

column of Table XV show the effects on regional lumber

outputs that is likely to result from a unit increase in

variables listed in the first column.

TABLE XV

IMPACT MULTIPLIERS FOR SELECTED EXPLANATORY VARIABLES: REGIONAL LUMBER OUTPUT

(Measured as % of Total Consumption)

NW SO SW IL Housing starts •••• : 0.0035 0.0024 0.0018 0.0011

(xl000) Personal income ••• : 0.0174 0.0132 0.0085 0.0044

(MMM 1972 $) Average lumber price in U.S •••••• : 0.218 0.152 0.149 0.067

(1967 $ / MBFt.) Regional lumber prices •••••••••••• : -0.218 -0.152 -0.149 -0.067

(1967 $ / MBFt.) Regional stumpage prices •••••••••••• : -0.120 -0.110 -0.119 -0.085

(1967 $ / MBFt.) PPI wood products freight ........... : -0.0035 -0.0014 -0.0013 -0.0011

(1967 = 100)

CAN 0.0059

0.0237

0.1090

0.0160

These multipliers are also the mechanisms by which

changes in aggregate consumption can be allocated across

producing regions. This can be illustrated by an example.

Suppose there is an increase of one thousand units in

national housing starts. From equation (1), Table VIII, we

94

would expect a corresponding increase, on the average, of

approximately 5.1 MMBFt. in total lumber consumption. The

multipliers in the first row of Table XV, can now be used to

determine how such increase in aggregate demand will be

allocated across producing regions. The results show that on

the average, holding all other variables constant, such an

increase in national housing starts would lead to increases

of 1.2, 0.9, 0.61, 0.47, and 1.98 MMBFt. respectively in the

NW, SO, SW, IL, and Canadian imports. Due to errors in

coefficient estimates, the total does not add to 5.1 MMBFt.

The discrepency, however, is negligible and can be corrected

by proportional adjustment of multipliers. This procedure

can b~ appli~d to determine the relative impacts on regional

market shares of unit change in these variables. Regional

market share impacts for selected variables are reported in

Table XVI.

The dynamic context of the present model and inter­

dependencies that are built into it, limit the usefulness of

analysing multipliers in a static setting. These multipliers

do, however convey important descriptive information on

parameter estimates and behavioral consistency of individual

relationships. Examination of impact multipliers in Tables

XV and XVI, for example, reveals some interesting patterns

of differential response to various exogenous factors across

the four domestic supply regions.

It is apparent from these results that short-run

impacts on market shares of the variables considered here

95

TABLE XVI

IMPACT MULTIPLIERS FOR SELECTED EXPLANATORY VARIABLES: REGIONAL JGUMBER MARKET SHARES

NW SO SW IL CAN Housing starts.: .00059 -.00051 -.00116 -.00176 .00294

(x1000) Personal income: .0039 -.00018 -.0050 -.0091 .0100

(MMM 1972 $) Average lumber price in u.S ••• : .0790 .0130 .0100 -.0720 -.0300

( • 67 $ /MBFt.) Regional lumber prices ••••••••• : -.2180 -.1520 -.1490 -.0670 -.0160

( • 67 $ /MBFt.) Regional stump. prices ••••••••• : -.1200 -.1100 -.1190 -.0850

( • 67 $ /MBFt.) PPI Wood Prod. freight •••••••• : -.00167 .00043 .00052 .00072

(1967 = 100)

are generally quite small. The NW, however, appears to be

relatively more sensitive to these exogenous impacts than

other regions. Market shares for the NW appear to be

particularly sensitive to transport costs. In the case of

the SW region, the magnitude of some impacts --particularly

those associated with transport costs and price variables-­

are somewhat higher than expected. For a net importing

region such as the SW, it is indeed reasonable to expect the

market share to be inversely related to accessibility. Such

expectation is justified because a decline in transport

costs (i.e. increased accessibility) can in effect make the

region itself more accessible to other producing regions and

invite competition.

96

A possible explanation for the observed sensitivity of

the SW market shares to accessibility lies in the species

composition of the region's lumber products. Redwood, which

constitutes a large portion of the lumber produced in the SW

region, is a specialty product in demand in all other

regions in the country. Thus, though a net importer of

lumber products; the region has historically exported

considerable volumes of redwood to other regions.

As indicated in Chapter I, the coefficients on price

terms in market share relationships measure the degree of

competitiveness and reflect the extent of regional

substitution in the product market. If products from

competing regions are perfect substitutes, then small

changes in relative prices in one region can be expected to

result in large changes in the demand facing that region. As

evidenced by the low elasticities on price terms (ranging

between 0.02 for the NW and 0.1 for the SW), this clearly is

not the case in the lumber market. The low price responsive­

ness of regional market shares found here suggest that the

extent of regional sUbstitution in the lumber market is

indeed quite limited.

In view of the low price elasticities of regional

lumber supplies (ranging from 0.08 for the NW and 0.15 for

the SO), this finding is not all too surprising. A more

serious implication here is that this finding also casts

doubt on the validity of the product homogeneity assumption.

There is no doubt that consumers' species preferences has

97

some influence on determination of demand for lumber

produced in specific regions. The extent of this influence,

however, cannot be deduced directly within the context of

the present model.

Price elasticities of demand for regional plywood, on

the other hand, are significantly greater than those found

for lumber, indicating a much higher level of competitive­

ness in this market. Estimated elasticities indicate that a

one percent change in plywood price ratios can be expected

to lead to 1.3 and 2.0 percent change, respectively, in

demand for plywood produced in the NW and the so.

V~DATION IN SIMULATION AND FORECASTING

Validity in simulation performance was used as the

primary guideline in evaluation of the model. As indicated

earlier, the objective in constructing the present model

was, in part, simulation analysis and forecasting. An

important test of the model's validi ty is, therefore, its

efficacy in serving these ends. To test the adequacy in

simulation performance of the model, we will first consider

the accuracy with which the model can replicate the actual

time paths of endogenous variables through a graphical

analysis of historical and simulated series; and then use

the model to develop proj ections of key variables for two

years beyond the estimation period.

A comparisons of actual and predicted series for all

enodogenous variables are shown in Figures 10 through 30.

~ • " ILC

III 0 l· l ~ t

.. 4J

42

41

40

311

J8

37

38

35

34

33

J2

31

JO

29

25

98

51 53 55 57 511 81 83 55 87 811 71 73 75 n 711 81 83

- Aclual + P...s1cI..t

Figure 10. Historical simulation total lumber consumption.

lJO~----------------------------~--------------~

120

110

100

90

80

51 53 55 57 511 8' 8l as 87 eg 71 73 75 77 711 8' IIJ

Figure 11. Historical simulation average lumber price.

99

21

20

19

111

17

18

15

14

13

12

11

10

9

S

7

8

5

4

3

2

51 53 55 57 58 81 a3 as 87 ee 71 73 75 77 78 81 83

Figure 12. Historical simulation total plywood consumption.

8 I ~ ii • " .5

~~-----------------------------------------------,

320

300

280

260

240

220

200

1110

160

140

120

51 53 55 57 58 81 a3 as 87 88 71 73 7!l n 79 111 a3

- Actual + Pr.dIc:tM

Figure 13. Historical simulation PPI softwood plywood.

... m

eo.-------------------------------------~------_,

55

45

:1 .a " .. " .. 35 (I

30

25

20

- Actual + PNdcbod

Figure 14. Historical simulation stumpage price NW.

... m :1

~ r­CI (I

2a,-------------------------------------------~~

27

25

25

24

23

22

21

20

10

15

17 iii I I • I • iii.

51 53 55 57 50 51 53 55 51 ell 11 13 75 n 711 III 53

- Actual

100

Figure 15. Historical simulation stumpage price so.

~~--------------------------------------~-------~

45

40

25

20

51 53 55 51 5. 81 113 55 81 811 11 13 75 n 79 81 113

- Actual + P...-.:ted

Figure 16. Historical simulation stumpage price sw .

It.. III :I "­.. " .. at

.#,'

~,------------------------------~------------~

28

28

24

22

20

111 i 111 i 14

12

10

II

:1~-r,,1-r"1-r"1-r"'-r, ~,~,~,~'~,~'-r,~'-r,~'-r,~'-r,~'-,rT'-'~'~I~'~I~' 51 53 55 57 511 81 113 115 117 1111 11 73 75 71 79 81 113

- Actual

101

Figure 17. Historical simulation stumpage price IL.

102

140

130

120

110 ... CD :2 "-• 100 .... .. ~

~

51 53 55 51 51 11 4J 85 111 811 11 13 15 n 79 111 III

- Actual

Figure 18. Historical simulation lumber price NW.

150

Al 140

130 I

... CD 120 :2 "-• .... ..

110 ~

51 53 55 51 5' 111 III 115 81 III 11 13 75 71 7' 111 III

- Actuat

Figure 19. Historical simulation lumber price so.

103

leo~----------------------------------------,

150

140

lJO "-III Ji "-.. 120 ... .. ~

110

100

, ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , I 110 51 53 55 57 51 81 III 85 87 81 71 73 75 77 7a 81 III

- Actual + Predicted

Figure 20. Historical simulation lumber price sw.

lJO

120

110

"-III :J "-.. 100 ... .. ~

"~ :l~,

51 53 55 57 sa 81 III 85 87 sa 71 73 75 77 7a '" III

- Actual

Figure 21. Historical simulation lumber price IL.

8 I

" " at

• • " E

8 I

" " ~ x • " S

'~.r--------------------------------~----------~

140

130

120

110

100

140

130

120

110

100

90

eo~ I

70 J I

1501 51

Actual

Figure 22. Plywood price Douglas fir.

57 511

Actual

f\, \ / \

I

'/

81 83

+ Pro6:I ...

85 87 811

Figure 23. Plywood price Southern pine.

104

c 2 a. E , • c o o a ~

32 -----------_. __ .

51 53 55 57 5a 111 III 115 87 ea 71 73 75 n 7a 111 III

- Actual

Figure 24. Lumber market share Canada.

RIIS EtTo ... l.35 3a,------------------------------------------------~

c

J8

37

J8

35

l4

o Jl ::: e J2 , ~ 31 o o JO

29

21S

27

211

25 1 24 -l

I

23 -l 22 I

~\ ! ~ I

.,.,.,.,.,.,.,.,.,.,.,.,.,~ 51 53 55 57 5a 111 III e 117 sa 71 73 75 77 7a lSI III

- Actual + Pred1ctod

Figure 25. Lumber market share NW.

105

c o :> Go E , • c o U

o ~ It

c ~ D-E , • c 0 U

0 ~ It

106

NIlS Emw-o.71 29~----------------------------------------------,

21!

27

28

24

23

22 21

20

10 ~ fl. 1'1 iii

51 53 55 57 58 81 83 85 87 69 71 73 75 77 79 I!I 1!3

- Adual

Figure 26. Lumber market share so.

MIS Emw-o.71 HI

II!

17

11!

51 53 55 57 511 81 1!3 as 87 811 71 73 75 n 711 81 1!3

- Actual

Figure 27. Lumber market share SW.

c o ., Do E , • c a (J

a o 0-

It

c a ., Do E , . c a (J

a ~ It

:: ~ 121 11

10

II

II

Sl !SJ SS 57 511 81 113 lIS 87 8e 71 73 75 n 78 111 113

- Actual + Preclc:ted

Figure 28. Lumber market share IL.

RIolS Erro.-2.2 115

110

~ 7S

70 \ , ~ 55

80

S5

:L 51 !SJ SS S7 511 81 III lIS 87 811

Actual + ""-dIeted

Figure 29. Plywood market share NW.

107

71

RMS ErTor-2.6 60~--------------------------------------------~---,

:;0

~ ~ .. Q.

E , . ~ 30 u "0

~ I( 20

10

51

10

II

II

7 c a .. Q. II E , . c 5 a 0

"0

~ 4

Ie 3

2

53 55 57 59 111 153 115 117 69 71

Actual + PredIcted

Figure 30. Plywood market share so.

RI.IS Enot - O.gS

+ ProodIcted

Figure 31. Lumber market share North

108

109

For the seven key variables, i.e. regional lumber and

plywood market shares, "root-mean-square" (rms) simulation

errors are also reported.

In general, the results of ex post simulations appear

to support the overall structure of the model. Nearly all

simulated series seem to track the principal trends closely

and, in most cases, replicate the timing of turning points

accurately. In the aggregate market, the results for total

product consumption are superior to product price outcomes

for both lumber and plywood. simulations of regional

stumpage and product prices are of mixed quality. Although

in all cases long-run trends are closely approximated, in

several instances such as stumpage prices in the NW and so

short-run fluctuations and the timing of several peaks and

troughs are poorly depicted.

In evaluating the simulation performance of the model,

the heaviest weight was given to regional market share

variables. Because of their pivotal role, and the fact that

market shares consti tute the primary output of the model,

the ultimate validity of the entire model is decided by the

performance of these relationships. In judging the accuracy

of market share predictions, it is important to recognize

the serious implications of bias in terms of actual quanti­

ties. A seemingly negligible error in these variables, once

translated into product quantities, can lead to unacceptable

results in estimates of regional outputs.

110

Historical simulations for regional market shares are

shown in Figures 25 through 30. A graphical comparison of

these results, shows that in all cases historical trends are

reproduced remarkably well. The relatively low rms errors in

these simulations also verify this conclusion. However, in a

model designed for short-run projections, it is also

essential that short term fluctuations be approximated

accurately. As evidenced by the simulation results, it is

apparent that in some cases this condition is not satisfied

as fully as we would have liked.

In general, the results obtained for Canada, NW, and

sw appear to be much more representative of the historical

behavior than those found for other regions. For the last

several years of the sample period, South's shares of lumber

and plywood markets are both under estimated. In the case of

the IL lumber market shares, many short term fluctuations

are either missed or represented with delay.

The untimely simulation of short term peaks and

troughs of historical series appears as a common problem in

several market share relationships. This problem is, in

part, attributable to the autoregressive structures of

market share relationships. In all cases, however,

deviations from actual values are very small in absolute

magnitude and can be corrected by making minor adjustments

in few parameters of the model.

The historical trend in the share of the North region

in the lumber market is shown in Figure 31. Since the region

111

was not included in the model, the predicted values were

derived by subtracting cumulative market shares of other

regions in each period from 100 percent. It is important to

note that since market shares for this region are determined

exogenously, discrepencies between the predicted and actual

values represent the magnitude of total error in market

share equations. comparison of actual and simulated series,

as shown in Figure 31, show that the cumulate error in

market share estimates is indeed negligible.

As a final check on the performance of the model as a

whole, the complete model will be simulated forward for two

years beyond the estimation period. This ex post forecasting

exercise has the two-fold purpose of showing the predictive

accuracy of the model, and providing a means for judging the

overall utility of the model as a forecasting tool.

Values for nearly all exogenous variables for both

years are available from same sources as listed in Appendix

A. Also available, are the 1985 values for certain key

endogenous variables such as aggregate consumption and

regional outputs. Thus it is posssible to compare model

projections with known values of certain variables. S:tnce

1986 values for some exogenous variables were not available,

it was necessary to use estimated values derived under

certain assumptions. For instance the national forest

offerings were held constant at the 1985 level. Change in

output per employee for all regions were assumed to continue

112

TABLE XVII

PROJECTED VALUES FOR MAJOR SOFTWOOD LUMBER AND PLYWOOD MARKET VARIABLES

Variable 1984 1985 1986 Total Lumber Cocsumption •• : 43021 44207.4*

(44204) 45867.3

Average Price for lumber ••• : 81. 79 79.82 88.17

Total plywood consumption •• : 19508 22735 23618.3

(22838) PPI softwood plywood •••••• : 303.5 307.2 314.9

(302.9) Average lumber price NW ••.•• : 77.70 73.35 84.90

Average lumber price SO ••••• : 99.40 104.7 109.0

Average lumber price SW ••••• : 110.29 106.2 114.9

Average lumber price IL ••••• : 81.40 75.13 74.70

Plywood production NW: 8319.2 8281. 9 8319.2

(8395.5) Plywood production SO: 10351.7 11406.4 11912.6

(11033.8) Mkt. share lumber Canada: 30.80 32.50 33.48

(33.04) Mkt. share lumber NW •••• : 23.41 24.45 24.20

(23.21) Mkt share lumber SO •••• : 24.75 25.14 25.02

(24.54) Mkt. share lumber SW •••• : 8.86 9.30 8.71

(8.79) Mkt. share lumber IL •••• : 9.37 10.39 10.50

(10.32)

* Figures in parantheses show actual values.

113

at their average historical rates in all regions; and the

price of Canadian lumber was estimated at a level commen­

surate with the Producer Price Index for all softwood

lumber.

The two-year projections for aggregate levels of

consumption and prices for both lumber and plywood, and

regional product prices and market shares are shown in Table

XVII. Plywood price index and regional product and stumpage

prices were all estimated from reduced form equations so

that current endogenous variables were eliminated from the

right-hand side of these equations.

A comparison of proj ected and actual values of the

main market variables in 1985 indicates that nearly in all

cases the actual values are closely approximated. The major

exception is the regional plywood market. Plywood production

in the NW is slightly underestimated, while production in

the SO is overestimated by nearly 400 million square feet

(1.6 percent of total consumption). PPI for softwood plywood

also appears to miss the 1985 mark by six points.

During this two year period, the projected trend is

one of increasing demand in both lumber and plywood markets

stimulated by the surge in the national housing market. with

the exception of the southern pine lumber, 1985 product

prices are projected to fall below their 1984 levels and

then increase slightly in 1986.

projected pattern for regional market shares in lumber

show that increases in quanti ties of lumber consumed will

114

not be distributed evenly across producing regions. As

indicated by resul ts in Table XVII, domestic producers'

shares of the lumber market are expected to remain largely

stable. Canadian producers appear as the single most

important beneficiary of the increased demand for lumber.

The market share outcomes suggest that nearly all of the

anticipated increments in demand for lumber will be

satisfied by Canadian imports; thus adding to the prominence

of Canada as the major supplier of lumber in the u.s.

market.

Canada's role in the domestic lumber market is,

however, sensitive to price conditions both in Canada and in

the u. S. Shifts in the delivered prices of the Canadian

lumber are likely to take place as a result of changes in

exchange rates and/or imposition of tariffs. In view of

recent trends in the international currency market, and the

current debate over the imposition of tariff on the Canadian

lumber imports, the position of Canada in the u.S. lumber

market is likely to undergo some change in the future.

The results of the present study indicate, for

example, that imposition of a 20 percent ad valorem duty on

lumber imports can result in a 0.75 percent (350MM BFt.)

reduction in Canada's share of the lumber market in the

first year. Such impact, however, is not likely to persist

in future periods. The magnitudes of future period impacts

also depend on price conditions in the u.S. For one thing,

any such change in the delivered price of the Canadian

115

lumber will also lead to increased average prices in the

u.s. (and possibly some reduction in quantities demanded).

We can therefore expect the initial period price disad­

vantage arising from the imposition of tariffs to be some­

what mitigated in the following periods so that the overall

impact on market shares will not be very large.

CONCLUDING REMARKS

This research was motivated by an interest in

exploring the mechanisms that underlie the geographical

distribution of production in the lumber and wood products

industry as a specific case in the broader context of

spatial competition. The research is a further step in the

ongoing efforts in regional modeling, and provides a

framework for the explicit treatment of linkages between the

national and regional economies. In addressing this problem,

we opted for an econometric approach as a compromise between

the oversimplicity of some conventional methods of location

analysis and the complexity of mathematical programming.

The design of the model was guided by the three-fold

objective of developing a model that accurately describes

the behavior of the two industries and their spatial

characteristics, can provide reliable projections of short

term trends, and serve as a tool in simulation experiments.

The overall performance of the model bears witness to

the fact that all three objectives were met, though with

varying degrees of success. with respect to the approach

116

adopted here, it has been shown that it is indeed a viable

one. The findings provide ample evidence in support of the

initial postulates of the study regarding the determinants

of regional market shares.

In several areas, however, there is room for some

refinements that can improve the effectiveness of the

approach. There is, first of all, the specification of

spatial units that can be better presented by further

disaggregation. For example, more homogeneous spatial units

can be created by separate treatment of the Coastal and

Inland parts of the Northwest region; and independent

presentation of the Southeast and Southcentral regions. with

further experimentation, and using more appropriate measures

of product demand such as housing starts, alternative

accessibility indexes can be constructed to better represent

regional locational advatage.

Since a primary point of interest in this undertaking

was development of the approach itself and testing of its

validity, much emphasis was placed on the statistical

properties of the model. This, combined with efforts to

maintain theoretical consistency in behavioral relation­

ships, led to certain rigidities in the structure that

complicate the forecasting and simulation processes. A

further problem in forecasting application arises from the

frequent appearance of lagged endogenous variables in the

model which can lead to efficiency problems in extended

forecasts.

117

Further extensions along the product dimension of the

model are also possible. The pulpwood sector might, for

instance, be included in the model so that a more complete

picture of competition in regional stumpage markets is

obtained. These and other extensions of the model are,

however, contingent upon availability of data at the

regional level, a persistent problem in all regional

modeling efforts including the present one.

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APPENDIX A

DATA SOURCES

1 - Adams, D.M., K.C. Jackson, and R.W. Haynes (1986) "Production, Consumption and Prices of Softwood Products in North America: Regional Time Series Data, 1950-1985". Unpublished Report, USDA/FS, Pacific Northwest Forest and Range Experiment station, Portland, Or.

125

2 - USDA-Forest service, Pacific Northwest Research Station, Production, Prices, Employment, and Trade in the Northwest Forest Industries. Resource Bulletin, PNW-13 0 , [quarterly issues]. Portland, Ore.

3 - National Forest Products Association, Fingertip Facts and Figures. [monthly], Washington, D.C.

4 - USDC, Business and Defense Service Admin. U.s. Lumber Exports: 1953-1966. 1968.

5 - USDC, Bureau of the Census, County Business Patterns. [annual issues].

6 - USDC, Bureau of the Census, "Lumber Production and Mill Stocks", Current Industrial Reports, Series MA-24T [annual].

7 - American Plywood Association, "structural Panel Produuction by States". Bulletin FA-235, [annual], Tacoma, Wa.

8 - Economic Report of the President. U.s. Gov. Printing Office, 1985.

9 - USDL, Bureau of Labor Statistics, Employment and Earnings. [monthly].

10- U.s. Federal Reserve System, Federal Reserve Bulletin. [monthly].

11- USDC, Bureau of the Census, "Value of New Construction Put in Place in the U.s.", Construction Report Series C30-80S.

12- USDL, Bureau of Labor statistics, Employment and

126

Earnings, states and Areas, 1939-1978., and Supplements.

13- USDA, Forest Service, U.S. Timber Production, Trade, Consumption. and Price statistics, 1950-84. Miscellaneous Publication No. 1442.

14- USDL, Bureau of Labor Statistics, Producer Price and Price Indexes. [monthly and annual].

15- USDC, Bureau of the Census, statistical Abstracts of the united States. [annual].

16- USDL, Productivity Measures for Selected Industries. Bulletin No. 2256.

17- USDC, Bureau of the Census, "Housing Starts", Construction Report Series C-22.

18- USDC, Bureau of the Census, U.S. Exports, Schedule E Commodity by Country. FT-410. [monthly and annual supplements].

19- USDA, Forest Service, "Volume and Value of sawtimber Stumpage Sold From National Forests by Selected Species and Regions". [quarterly and annual].

APPENDIX B

TABLE XVIII

AVERAGE HOURLY EARNINGS IN MANUFACTURING AND LUMBER & WOOD PRODUCTS (Current U.S. $)

Manufacturing SIC 24 ---------------------------- ----------------------------

Year US NW SO SW IL US NW SO SW IL

1950 1. 42 1. 76 1.18 1. 65 1.57 1.35 1.67 1.12 1.57 1.49 1951 1.53 1.91 1. 27 1.77 1.68 1.47 1.83 1. 22 1. 70 1.61 1952 1.67 2.01 1.33 1.87 1. 77 1.55 1. 87 1. 23 1. 74 1. 64 1953 1.77 2.07 1.40 1.97 1.86 1.62 1.89 1.29 1.80 1. 70 1954 1.81 2.13 1.45 2.03 1.91 1.63 1.91 1. 30 1.83 1.72 1955 1.89 2.22 1.50 2.11 1.99 1.68 1.97 1. 34 1.88 1. 76 1956 1.98 2.29 1.62 2.22 2.10 1. 76 2.04 1. 44 1.97 1.87 1957 2.07 2.34 1. 71 2.32 2.17 1.81 2.04 1. 50 2.03 1.90 1958 2.13 2.42 1. 76 2.44 2.24 1.89 2.15 1. 56 2.17 J .98 1959 2.22 2.52 1.82 2.53 2.33 1.97 2.23 1. 62 2.25 2.07 1960 2.29 2.59 1.89 2.62 2.40 2.07 2.34 1. 70 2.37 2.17 1961 2.35 2.66 1.93 2.72 2.46 2.11 2.38 1. 73 2.44 2.21 1962 2.38 2.74 2.02 2.80 2.54 2.14 2.46 1.81 2.52 2.28 1963 2.46 2.76 2.05 2.86 2.62 2.15 2.41 1. 79 2.50 2.29 1964 2.53 2.91 2.14 2.94 2.67 2.16 2.48 1.83 2.51 2.28 1965 2.61 3.00 2.20 3.02 2.75 2.18 2.51 1.84 2.52 2.30 1966 2.70 3.14 2.30 3.12 2.82 2.26 2.63 1.92 2.61 2.36 1967 2.82 3.27 2.39 3.25 2 :96 2.38 2.76 2.02 2.74 2.50 1968 2.99 3.42 2.56 3.40 3.10 2.53 2.89 2.16 2.88 2.62 1969 3.18 3.65 2.72 3.57 3.23 2.72 3.12 2.32 3.05 2.76 1970 3.36 3.98 2.91 3.81 3.48 2.98 3.53 2.58 3.38 3.08 1971 3.55 4.26 3.07 4.06 3.68 3.12 3.74 2.70 3.57 3.23 1972 3.77 4.42 3.14 4.23 3.91 3.25 3.81 2.71 3.65 3.37 1973 4.04 4.75 3.47 4.45 4.13 3.61 4.24 3.10 3.98 3.69 1974 4.37 4.99 3.70 4.59 4.45 3.87 4.42 3.28 4.06 3.94 1975 4.78 5.52 4.10 5.10 4.88 4.25 4.90 3.65 4.53 4.33 1976 5.15 6.01 4.43 5.46 5.30 4.66 5.43 4.01 4.94 4.80 1977 5.07 6.53 4.80 5.87 5.76 5.60 7.21 5.30 6.48 6.36 1978 5.61 7.53 5.39 6.47 6.77 6.07 8.15 5.84 7.00 7.33 1979 6.67 8.19 5.84 7.10 7.04 6.15 7.55 5.38 6.55 6.49 1980 7.18 8.85 6.35 7.60 7.68 6.55 8.07 5.79 6.93 7.01 1981 7.97 9.84 7.02 8.41 8.30 7.09 8.75 6.24 7.48 7.38 1982 8.50 10.69 7.65 9.25 9.01 7.54 9.48 6.78 8.21 7.99 1983 8.79 10.89 7.99 9.51 9.42 7.84 9.71 7.13 8.48 8.40 1984 9.14 11.00 8.28 9.75 9.66 8.02 9.65 7.27 8.56 8.47 ----------------------------------------------------------------Source: Mfg, Appendix A, (9] ; Lumber & Wood Prod., 1972-84, App.

A, (12], 1950-71 see page 80 of text for derivation.

APPENDIX C

TABLE XIX

INDEX OF LABOR PRODUCTIVITY IN LUMBER AND PLYWOOD PRODUCTION (1967=100)

Lumber Plywood --------------------------------------- ------------------Year US NW SO SW IL US NW SO

1950 0.46 0.00 0.00 0.00 0.00 0.41 0.53 0.00 1951 0.43 0.47 0.46 0.48 0.43 0.40 0.55 0.00 1952 0.48 0.55 0.47 0.56 0.51 0.42 0.58 0.00 1953 0.50 0.64 0.44 0.65 0.58 0.44 0.61 0.00 1954 0.55 0.70 0.48 0.71 0.64 0.46 0.64 0.00 1955 0.53 0.76 0.49 0.77 0.69 0.47 0.66 0.00 1956 0.56 0.81 0.52 0.83 0.74 0.51 0.69 0.00 1957 0.58 0.85 0.54 0.86 0.77 0.55 0.72 0.00 1958 0.63 0.88 0.56 0.90 0.81 0.59 0.75 0.00 1959 0.68 1.01 0.78 1.03 0.92 0.63 0.77 0.00 1960 0.71 0.92 0.59 0.93 0.84 0.64 0.78 0.00 1961 0.76 0.95 0.59 0.97 0.87 0.71 0.82 0.00 1962 0.71 0.92 0.65 0.93 0.84 0.70 0.82 0.00 1963 0.86 0.99 0.77 1.00 0.90 0.78 0.87 0.00 1964 0.93 1.04 0.89 0.95 0.96 0.86 0.96 0.86 1965 0.93 1.06 0.98 0.96 0.94 0.91 0.99 0.91 1966 0.96 0.98 0.97 0.98 0.91 0.92 0.95 0.92 1967 1. 00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

. 1968 1.06 1.14 1.05 1.11 0.97 1.07 1.01 1.07 1969 1.00 0.96 1.03 1.02 0.90 0.99 0.95 0.99 1970 1.03 1.01 1.02 1.10 0.97 1.09 1.06 1. 09 1971 1.15 1.06 1.20 1.11 1.02 1.22 1.12 1. 22 1972 1.17 1.03 1.17 1.12 0.97 1. 23 1.16 1. 23 1973 1.18 1.03 1. 08 1.07 0.98 1.17 1.11 1.17 1974 1.11 1.02 0.95 0.92 0.86 1.05 1.08 1. 27 1975 1.09 1.09 1. 25 1.01 1.09 1.30 1.29 1. 65 1976 1.19 1.12 0.87 1.06 1.04 1. 34 1.41 1.94 1977 1.18 1.15 1.17 1.04 0.97 1.49 1.34 2.14 1978 1.16 1.12 1.02 0.99 0.96 1. 52 1.32 2.20 1979 1.13 1.05 1.11 1.00 0.98 1. 55 1. 25 2.26 1980 1.08 0.92 0.96 0.81 0.97 1.47 1.19 2.26 1981 1.05 0.97 1.42 0.81 1.05 1.56 1.34 3.04 1982 1.05 1.06 '1.30 0.85 1.16 1.57 1.33 3.31 1983 1. 32 1.34 1.43 1.06 1.19 1.60 1. 54 3.32 1984 1. 30 1.23 1.80 0.95 1.12 1.57 1.54 3.34 ------------------------------------------------------------Constructed from output/man-year estimates for each region. Source: See Appendix A, (1] , (5], and (6].

APPENDIX 0

TABLE XX

PRODUCER PRICE INDEX: TRANSPORTATION SERVICES AND LUMBER & WOOD PRODUCTS FREIGHT

Year

1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984

Trans. Service 67=100

53.30 58.30 62.40 66.40 69.20 69.40 70.50 73.80 78.50 81.20 83.30 85.30 86.60 87.50 89.60 92.90 96.80

100.00 104.00 111. 30 123.10 133.00 136.00 136.90 141. 90 152.70 174.30 188.40 197.40 212.80 242.60 271. 60 294.40 303.60 313.80

Lum. & WP Freight 69=100

47.89 52.38 56.06 59.66 62.17 62.35 63.34 66.31 70.53 72.96 74.84 76.64 77.81 78.62 80.50 83.47 86.97 89.85 93.44

100.00 108.40 119.00 123.30 127.40 147.40 163.60 177.90 191. 70 205.70 233.80 273.90 320.50 350.60 355.00 382.50

-------------------------------------------------Source: Transportation Services, Appendix A, [14]. Lum & WP Freight, 1969-84, Append. A, [14]; 1950-68 derived from regression PPIWPF = -32.57 + 1.265 *(PPI Transp. Services).